Compatible Actions Research Articles

Finite approximation properties of C*-modules III

Abstract We introduce and study a notion of module nuclear dimension for a C * \mathrm{C}^{*} -algebra A which is a C * \mathrm{C}^{*} -module over another C * \mathrm{C}^{*} -algebra 𝔄 {\mathfrak{A}} with compatible actions. We show that the module nuclear dimension of A is zero if A is 𝔄 {\mathfrak{A}} -NF. The converse is shown to hold when 𝔄 {\mathfrak{A}} is a C ⁢ ( X ) {C(X)} -algebra with simple fibers, with X compact and totally disconnected. We also introduce a notion of module decomposition rank, and show that when 𝔄 {\mathfrak{A}} is unital and simple, if the module decomposition rank of A is finite then A is 𝔄 {\mathfrak{A}} -QD. We study the set 𝒯 𝔄 ⁢ ( A ) {\mathcal{T}_{\mathfrak{A}}(A)} of 𝔄 {\mathfrak{A}} -valued module traces on A and relate the Cuntz semigroup of A with lower semicontinuous affine functions on the set 𝒯 𝔄 ⁢ ( A ) {\mathcal{T}_{\mathfrak{A}}(A)} . Along the way, we also prove a module Choi–Effros lifting theorem. We give estimates of the module nuclear dimension for a class of examples.

The Effect of Wearable and Tearable Climate and Weather on Wearable Technology

This article discusses the effect of wearable tearable climate and weather on wearable technology. Climate change refers to long term shifts in temperature and weather patterns, mainly caused by human activities, especially the burning of fossil fuels and unsustainable infrastructural development. Strategic environmental assessment (SEA) process can be broadly defined as a study of the impacts of a proposed project, plan, project, policy, or legislative action on the environment and sustainability. The significance of the work entitled “Sustainable Wearable Climate and Weather Management” is mainly confirmatory as it solves environmental and social problems. In this research, the SEA process has been aimed to incorporate environmental and sustainability factors into wearable climate and weather management includes climate change and control as an example like production and manufacturing process project planning and decision-making processes such as project formulation and appraisal of wearable climate and weather projects like wear and tear of dust-producing grinding chrome composite leather clad rollers and washers commonly used in seed-cotton Indian roller ginning machines, wastewater treatment process, rotating biological contactors, trickling filter bed, biomedical parts, marine biopolymers, Indo-Matsushita midget electrode (battery carbon rod) plant in 1979 at Tada, sustainable bridge, road, and sanitation structure, green building, nuclear power plant, cotton roller ginning plant and concrete that included policies, programs, plans, and legislative actions. Sustainable materials for manufacturing process development is a kind of development that meets the needs of the present without compromising the ability and efficacy of future generations to meet their own needs. Environmental Impact Assessment (EIA) process can be defined as the systematic study of the potential impacts (effects) of proposed projects, plans, programs, policies, or legislative actions relative to the physical-chemical, biological, bio-medical, cultural, and socioeconomic components of the total environmental product life cycle. The primary purpose of the EIA process is to encourage the consideration of the environment in the Organizational ’s wearable and tearable climate and weather management project planning and decision-making process and to arrive at environmentally compatible actions. The sustainable wearable climate and weather management process should include the integrated consideration of technical or engineering, economic, environmental, safety, and health, social, and sustainability factors to achieve business excellence as per post COVID-19 World Scenario. Before the National Environmental Policy Act (NEPA) process in 1970 in the USA, technical and economic factors dominance the World’s manufacturing process projects. The objective of the study is to conceptualize a training course module incorporating the SEA process for the Sustainable Environmental Wearable and Tearable Climate Change and Weather Control for the officers of Bihar Institute Public Administration and Rural Development (BIPARD), Patna, Bihar, India during the Research Year (RY) 2023-2024. The design of the study is cross-sectional. The limitation or recommendation of the study and check is to apply strategic environmental assessment process for sustainable environmental climate change and control towards sustainable development.

Finite approximation properties of $C^{*}$-modules II

We study quasidiagonality and local reflexivity for C^{*} -algebras which are C^{*} -module over another C^{*} -algebra with compatible actions. We introduce and study a notion of amenability for vector valued traces.

The effect of automatic imitation in serial movements with different effectors.

Individuals often imitate the postures or gestures of others in everyday life, without even being aware. This behavioral tendency is known as "automatic imitation" in laboratory settings and is thought to play a crucial role in social interactions. Previous studies have shown that the perception of a simple finger movement activates a shared representation of the observed and executed movements, which then elicits automatic imitation. However, relatively few studies have examined whether automatic imitation is limited to simple single-finger movements or whether it can be produced using a different automatic imitation paradigm with more complex sequential movements. Therefore, this study conducted three experiments in which participants observed the sequential movements of a model and then executed a compatible (similar) action or an incompatible (different) action involving the hand or foot in response to number cues that indicated the sequence for moving their hands or feet. The delay to onset of participants' initial hand or foot movements was calculated. Participants consistently executed compatible actions faster than incompatible actions. In particular, the results showed an imitative compatibility effect with a human stimulus but not an inanimate stimulus. These results demonstrate that automatic imitation occurs during more complex movements that require memory.

Global transfer systems of abelian compact Lie groups

Global transfer systems are equivalent to global N ∞ N_\infty -operads, which parametrize different levels of commutativity in globally equivariant homotopy theory, where objects have compatible actions by all compact Lie groups. In this paper we explicitly describe and completely classify global transfer systems for the family of all abelian compact Lie groups.

Formula omitted] modules of finite type on affine space

We study the category of modules admitting compatible actions of the Lie algebra V of vector fields on an affine space and the algebra A of polynomial functions. We show that modules in this category which are finitely generated over A, are free. We also show that this pair of compatible actions is equivalent to commuting actions of the algebra of differential operators and the Lie algebra of vector fields vanishing at the origin. This allows us to construct explicit realizations of such modules as gauge modules.

Global N∞$N_\infty$‐operads

AbstractWe define ‐operads in the globally equivariant setting and completely classify them. These global ‐operads model intermediate levels of equivariant commutativity in the global world, that is, in the setting where objects have compatible actions by all compact Lie groups. We classify global ‐operads by giving an equivalence between the homotopy category of global ‐operads and the partially ordered set of global transfer systems, which are much simpler, algebraic objects. We also explore the relation between global ‐operads and ‐operads for a single group, recently introduced by Blumberg and Hill. One interesting consequence of our results is the fact that not all equivariant ‐operads can appear as restrictions of global ‐operads.

Emergence of norms in interactions with complex rewards

Autonomous agents are becoming increasingly ubiquitous and are playing an increasing role in wide range of safety-critical systems, such as driverless cars, exploration robots and unmanned aerial vehicles. These agents operate in highly dynamic and heterogeneous environments, resulting in complex behaviour and interactions. Therefore, the need arises to model and understand more complex and nuanced agent interactions than have previously been studied. In this paper, we propose a novel agent-based modelling approach to investigating norm emergence, in which such interactions can be investigated. To this end, while there may be an ideal set of optimally compatible actions there are also combinations that have positive rewards and are also compatible. Our approach provides a step towards identifying the conditions under which globally compatible norms are likely to emerge in the context of complex rewards. Our model is illustrated using the motivating example of self-driving cars, and we present the scenario of an autonomous vehicle performing a left-turn at a T-intersection.

Finite approximation properties of C∗-modules

We study the notions of nuclearity and exactness for module maps on C∗-algebras which are C∗-module over another C∗-algebra with compatible actions and examine finite approximation properties of such C∗-modules. We prove module versions of the results of Kirchberg and Choi–Effros. As a concrete example, we extend the finite dimensional approximation properties of reduced C∗-algebras and von Neumann algebras on countable discrete groups to these operator algebras on countable inverse semigroups with the module structure coming from the action of the C∗-algebras on the subsemigroup of idempotents.

Equivariant Oka theory: survey of recent progress

We survey recent work, published since 2015, on equivariant Oka theory. The main results described in the survey are as follows. Homotopy principles for equivariant isomorphisms of Stein manifolds on which a reductive complex Lie group G acts. Applications to the linearisation problem. A parametric Oka principle for sections of a bundle E of homogeneous spaces for a group bundle {{mathscr {G}}}, all over a reduced Stein space X with compatible actions of a reductive complex group on E, {{mathscr {G}}}, and X. Application to the classification of generalised principal bundles with a group action. Finally, an equivariant version of Gromov’s Oka principle based on a notion of a G-manifold being G-Oka.

Global algebraic K‐theory

We introduce a global equivariant refinement of algebraic K-theory; here `global equivariant' refers to simultaneous and compatible actions of all finite groups. Our construction turns a specific kind of categorical input data into a global $\Omega$-spectrum that keeps track of genuine $G$-equivariant infinite loop spaces, for all finite groups $G$. The resulting global algebraic K-theory spectrum is a rigid way of packaging the representation K-theory, or `Swan K-theory' into one highly structured object.

Some homological results for amalgamated duplication of Banach algebras

Let [Formula: see text] and [Formula: see text] be two Banach algebras such that [Formula: see text] is a Banach [Formula: see text]-bimodule with the left and right compatible actions of [Formula: see text] on [Formula: see text]. Let [Formula: see text] be a strongly splitting Banach algebra extension of [Formula: see text] by [Formula: see text]. In this paper, we investigate some homological aspects such as injectivity, projectivity and flatness of [Formula: see text] and give some necessary and sufficient conditions for injectivity, projectivity and flatness of [Formula: see text].

Weak module amenability for the second dual of a Banach algebra

In this paper we study the weak module amenability of Banach algebras which are Banach modules over another Banach algebra with compatible actions. We show that for every module derivation D : A ↦ ( A/J_A )∗ if D∗∗(A∗∗) ⊆ WAP (A/J_A ), then weak module amenability of A∗∗ implies that of A. Also we prove that under certain conditions for the module derivation D, if A∗∗ is weak module amenable then A is also weak module amenable.

A “Lockdown” of Materialism Values and Pro-Environmental Behavior: Short-Term Effects of the COVID-19 Pandemic

The COVID-19 pandemic led to serious restrictions on peoples’ everyday lives and had severe economic impacts. In contrast, “lockdown” restrictions led to short-term beneficial effects for the environment. In the present study, we compared pro-environmental behavior and materialism values before, during, and after COVID-19 lockdown restrictions in the spring of 2020. The results of an online study using 370 participants showed a decrease in materialism values and pro-environmental sacrificing actions. In contrast, ecologically compatible actions decreased during the lockdown and increased again to the initial level after restrictions were loosened. Moreover, pro-environmental attitudes had a diminishing effect on materialism values, especially during lockdown restrictions. Agreeableness had a diminishing effect on materialism values during the lockdown. In contrast, trait narcissism enhanced materialism values, which were strongest after the lockdown was over. In conclusion, materialism values and pro-environmental behaviors were “locked down” due to COVID-19 restrictions but did not show the expected rebound effects. Practical and theoretical implications are discussed.

A U.S.‒China coal power transition and the global 1.5 °C pathway

As the world seeks to increase ambition rapidly to limit global warming to 1.5 °C, joint leadership from the world's largest greenhouse gas (GHG) emitters—the United States (U.S.) and China—will be critical to deliver significant emissions reductions from their own countries as well as to catalyze increased international action. After a period of uncertainty in international climate policy, these countries now both have current leadership that supports ambitious climate action. In this context, a feasible, high-impact, and potentially globally catalytic agreement by the U.S. and China to transition away from coal to clean energy would be a major contribution toward this global effort. We undertake a plant-by-plant assessment in the power sector to identify practical coal retirement pathways for each country that are in line with national priorities and the global 1.5 °C target. Our plant-by-plant analysis shows that the 1.5 °C-compatible pathways may result in an average retirement age of 47 years for the U.S. coal plants and 22 years for Chinese coal plants, raising important questions of how to compare broader economic, employment, and social impacts. We also demonstrate that such pathways would also lead to significant emissions reductions, lowering overall global energy-related CO2 emissions by about 9% in 2030 relative to 2020. A catalytic effect from the possibility of other countries taking compatible actions is estimated to reduce global emissions by 5.1 Gt CO2 in 2030 and by 10.1 Gt CO2 in 2045.

Extensions and dilations of module maps

We study completely positive module maps on C*-algebras which are C*-module over another C*-algebra with compatible actions. We extend several well known dilation and extension results to this setup, including the Stinespring dilation theorem and Wittstock, Arveson, and Voiculescu extension theorems.

ВІЙСЬКОВО-МОРСЬКІ СИЛИ ЗБРОЙНИХ СИЛ УКРАЇНИ ТА НАТО ЯК ОСНОВА БЕЗПЕКИ ТА СТАБІЛЬНОСТІ У ЧОРНОМОРСЬКОМУ РЕГІОНІ В АСПЕКТІ ФОРМУВАННЯ ВІЙСЬКОВО-ТЕХНІЧНОЇ ПОЛІТИКИ ДЕРЖАВИ

The article considers the issue of Cooperation of Ukraine with the North Atlantic Treaty Organization (NATO). Beginning in 2014, Ukraine is actually improving control with the use of international assistance in the security industry and the relevant reporting on operational and tactical levels. General activities of Ukraine and the Alliance in the direction of security and defence, objectives: transformation and strengthening of the national security and defence sector, in relation to the performance of inherent tasks, according to the interests of the country. To ensure regional, large-scale and stable security; to facilitate and improve the development of the Armed Forces of Ukraine; to involve Ukraine in the performance of tasks in accordance with the requirements of the state defence and participation in international operations; to achieve effective compatibility of the Armed Forces of Ukraine in the context of other component parts of defence and security to ensure the performance of tasks in international operations and exercises. After the annexation of the Crimea by the Russian Federation, the Armed Forces of Ukraine received significant assistance in 2014. The priority of joint activities with NATO is primarily to guarantee the alliance of the principle of collective defence, to preserve and strengthen peace and to ensure the prospect of future security. The Alliance's ability to perform strategic tasks depends on a high degree of coordination and planning of compatible actions at the political level of the defence sector. Analysis of the participation of the Naval Forces of Ukraine and the Alliance during joint international exercises and operations, the events of the war in 2014, the military aggression of the Russian Federation, the construction of relations between Ukraine and the United States during the armed conflict, adaptation of NATO standards and principles – a number of issues for the need for rapid solution in turbo mode. Based on the analysis, the authors conclude that it is legitimate and expedient to use and gain experience in the context of the concept of development of the Navy of the Armed Forces of Ukraine. Involvement and participation in multinational military exercises is a set of measures in the context of international military cooperation, which is allowed in conditions as close as possible to combat and real. Comprehensive improvement of the level of combat training of units of the Navy of the Armed Forces of Ukraine during the increase of the level of professionalism, combat readiness and combat ability. The necessity of introduction and application of compatible measures for performance of peacekeeping, humanitarian, search and rescue and other special tasks is the priority of the concept of modern Ukraine. Constant improvement of the combat readiness level in modern conditions is achieved during the international exercises for the necessity and possibility to strengthen the professional experience of partnership, which always fundamentally affects the quality of combat tasks ahead of the number of participants involved in joint activities. Keywords: NATO, Alliance, Ukrainian Navy, Armed Forces of Ukraine, standards, training, security, Charter.

Automatic Continuity of Derivations on Semidirect Products of Banach Algebras

Let $$\mathcal {A}$$ and $$\mathcal {U}$$ be Banach algebras such that $$\mathcal {U}$$ is also a Banach $$\mathcal {A}$$ -bimodule with compatible algebra operations, module actions and compatible norm. By defining an appropriate multiplication, we turn $$\ell ^1$$ -direct product $$\mathcal {A}\times \mathcal {U}$$ into a Banach algebra so that $$\mathcal {A}$$ is a closed subalgebra and $$\mathcal {U}$$ is a closed ideal of it. This algebra is, in fact, the semidirect product of $$\mathcal {A}$$ and $$\mathcal {U}$$ which we denote by $$\mathcal {A} < imes \mathcal {U}$$ . In this paper, we study automatic continuity of derivations on $$\mathcal {A} < imes \mathcal {U}$$ in a general setting. As an application of our results, we present various results about the automatic continuity of derivations of module extension Banach algebras and $$\theta $$ -Lau products of Banach algebras. Some examples are also given.

Gauge Modules for the Lie Algebras of Vector Fields on Affine Varieties

For a smooth irreducible affine algebraic variety we study a class of gauge modules admitting compatible actions of both the algebra \(\mathcal {A}\) of functions and the Lie algebra \(\mathcal {V}\) of vector fields on the variety. We prove that a gauge module corresponding to a simple \(\mathfrak {gl}_{N}\)-module is irreducible as a module over the Lie algebra of vector fields unless it appears in the de Rham complex.

PREFACE

Abstract. Without a doubt 2020 will be remembered worldwide as the year of risk and emergency, in this case a health emergency, and of new communication technologies. When work began in 2018 on the organisation of “HERITAGE2020 (3DPast | RISK-Terra), International Conference on Vernacular Architecture in World Heritage Sites. Risks and New Technologies”, the new technologies applied to vernacular heritage and risk were on the rise, although nobody could have foreseen how central they would become to everyday life in 2020. “HERITAGE2020 (3DPast | RISK-Terra), International Conference on Vernacular Architecture in World Heritage Sites. Risks and New Technologies” is organised within the framework of two research projects. The first, “3D Past – Living and visiting European World Heritage” (2017–2020), was co-funded by the European Union as part of the Creative Europe Programme, led by Escola Superior Gallaecia (Portugal) in partnership with Universitat Politécnica de València (Spain) and Università degli Studi di Firenze (Italy). The main aim of this project has been to promote the inhabited vernacular heritage declared as World Heritage Sites in Europe by trying to promote its valorization through new technologies, both for local residents and potential visitors. Vernacular heritage, new communication technologies and heritage management for valorization and sustainable tourism are the central themes of this European project. In 2020, these issues have become even more important for the survival, understanding and valorization of heritage, particularly vernacular heritage, which today provides a solid opportunity for cultural and sustainable tourism, where these new technologies make it possible to reach a wider public in search of locations better suited to social distancing. The second project involved in this conference is “RISK-Terra. Earthen architecture in the Iberian Peninsula: study of natural, social and anthropic risks and strategies to improve resilience” (RTI2018-095302-B-I00) (2019–2021), funded by the Spanish Ministry of Science, Innovation and Universities. This project is geared towards the conservation of earthen architecture in the Iberian Peninsula, both monumental and vernacular, which continues to be undervalued and barely recognized. The RISK-Terra project aims to provide scientific coverage of the study of natural threats (floods, earthquakes, climate change), social threats (abandonment, social discredit, demographic pressure, tourist development), and anthropic threats (neglect, lack of protection and maintenance), as well as the mechanisms for deterioration and dynamics and transformation (replacement, use of incompatible techniques and materials, etc.) to which architecture is exposed. The objective of the project is to establish strategies for conservation, intervention and rehabilitation which make it possible to prevent and mitigate possible damage through compatible actions and/or actions to increase resilience.As these two projects have major points of contact with potential for common reflection, their main themes have been combined in this Heritage2020 conference. The topics established for the conference are: vernacular architecture (study and cataloguing of vernacular architecture; conservation and restoration of vernacular architecture; urban studies on vernacular architecture; sustainability in vernacular architecture); new technologies applied to architectural and archaeological heritage (digital documentation and state-of-the-art developments; digital analysis in heritage; digital heritage related to social context; digital heritage solutions and best practices for dissemination); architectural heritage management (management and protection of UNESCO World Heritage Sites; social participation in heritage management; regulations and policies in heritage management; intangible heritage: the management of know-how and local building culture); risks in architectural heritage (studies of natural risks in architectural heritage; studies of social and anthropic risks in architectural heritage, preventive actions in order to improve resilience in architectural heritage; actions and strategies in post-disaster situations); earthen architectural heritage (study and cataloguing of earthen architectures; construction techniques that employ earth; sustainability mechanisms in vernacular earthen architectures; restoration and conservation of earthen architecture).The scientific committee was made up of 98 outstanding researchers from 29 countries from the five continents, specialists in the subjects proposed. All the contributions to the conference, both the abstracts and the final texts, were subjected to a strict peer-review evaluation system by the members of the scientific committee.Out of the over 300 proposals submitted, over 150 papers by 325 authors from 27 countries from the five continents were chosen for publication.