Compact Group Research Articles

Galaxy evolution in compact groups. II. Witnessing the influence of major structures in their evolution

Compact groups (CGs) of galaxies are an extreme environment for the morphological transformations and the cessation of star formation in galaxies. However, despite initially being conceived as isolated systems, it is now widely recognised that many of them are not as isolated as expected. Our objective is to understand the dynamics of CGs, as well as how the environment surrounding CGs impacts their morphological and physical properties. To achieve this, we selected a sample of 316 CGs in the Stripe 82 region, with a total of 1011 galaxies, and a sample of 2281 field galaxies as a control sample. We find that at least 41% of our sample of CGs are part of major structures, i.e. non-isolated CGs. We find a bimodality in the effective radius (R_e)-Sérsic index (n) plane for all transition galaxies (those with $(u-r) > 2.3$ and n<2.5) in CGs. Additionally, transition galaxies in isolated CGs populate more densely the R_e-n plane for n < 1.75. In contrast, transition galaxies in non-isolated CGs show a bimodal distribution in the R_e-n plane, with the n values smoothly increasing towards higher values, and 62% of these galaxies having n > 1.5. This indicates that the majority of these galaxies have already undergone a morphological transformation and primarily contribute to the population of more compact galaxies in the R_e-n plane. We find that galaxies in our sample of CGs have a lower mean specific star formation rate (sSFR) compared to the control sample, with non-isolated CGs showing even lower sSFR values, indicating that dense environments suppress star formation. Additionally, non-isolated CGs have a higher fraction of quenched galaxies relative to isolated CGs and the control sample. When dividing the sample by morphology, we find significant differences only for early-types galaxies (ETGs; those with $(u-r) > 2.3$ and n>2.5). In isolated CGs, ETGs show a lower fraction of quenched galaxies and higher sSFR in low-mass bins (log(M_*/M_ ⊙ ) < 11), suggesting they can maintain star formation. In contrast, ETGs in non-isolated CGs exhibit a higher fraction of quenched galaxies and lower sSFR in high-mass bins (log(M_*/M_ ⊙ ) > 11), underscoring the environmental impact on star formation suppression. Based on our results, we propose an evolutionary scenario where the major structures in which the CGs are embedded accelerate the morphological transformations of their galaxy members, and also facilitates preprocessing. Our findings highlight the importance of considering the larger structures in which CGs may be located, when analysing the properties of their galaxy members, as this can significantly affect the evolution of CGs and their galaxies.

Porosity in Lebesgue spaces regarding weighted convolution

In this paper, for some classes of weight functions [Formula: see text] on [Formula: see text], we study [Formula: see text]-[Formula: see text]-lower porosity of the set [Formula: see text] in [Formula: see text], where [Formula: see text] with [Formula: see text], [Formula: see text] is a compact symmetric neighborhood of the identity element of a locally compact group [Formula: see text], and [Formula: see text] is the weighted convolution between measurable functions on [Formula: see text].

MeerKAT view of Hickson Compact Groups. I. Data description and release

MeerKAT view of Hickson Compact Groups. I. Data description and release

MeerKAT view of Hickson Compact Groups:. II. deficiency in the cores and surrounding regions

Hickson compact groups (HCGs) offer an ideal environment for investigating galaxy transformation as a result of interactions. It has been established that the evolutionary sequence of HCGs is marked by an intermediate stage characterised by a substantial amount of in their intragroup medium (IGrM) in the form of tidal tails and bridges (phase 2), rapidly followed by a final stage in which no IGrM gas is found and i which their member galaxies are highly deficient (phase 3). Despite numerous single-dish and interferometric studies on the HCGs, a clear picture of the groups within their large-scale environment still remains to be uncovered. Taking advantage of MeerKAT's high column density sensitivity and large field of view, we aim to investigate the rapid transformation of HCGs from the intermediate to late phases, and establish a picture of their gas content variations in the context of their large-scale environments. We performed MeerKAT observations of six HCGs that were selected to represent the intermediate and late phases of the proposed evolutionary sequence. Combining the observations with data from recent wide-field optical surveys, we evaluated the deficiencies of galaxies in a ∼ 30'$ radius of the HCGs. We find that galaxies surrounding both phases exhibit similar distributions in their gas content. Similarly, galaxies making up the cores of phase 2 HCGs are comparable to their neighbours in terms of deficiencies. However, phase 3 groups are over an order of magnitude more deficient than their surroundings, supporting previous findings that late-phase HCG galaxies are more evolved than their large-scale environments.

A generalization of the Chermak–Delgado theorem to compact groups

We change Chermak–Delgado measure slightly so that it can be used for compact groups as well. Corresponding to this new measure, a lattice of open subgroups is obtained. Then we prove that if this lattice is non-empty in a compact group [Formula: see text], then [Formula: see text] has a characteristic open abelian subgroup [Formula: see text] such that [Formula: see text] for every abelian subgroup [Formula: see text]. This is a generalization of the well-known Chermak–Delgado Theorem.

Non-commutative skew-product extension dynamical systems

Abstract Starting from a uniquely ergodic action of a locally compact group G on a compact space $X_0$ , we consider non-commutative skew-product extensions of the dynamics, on the crossed product $C(X_0)\rtimes _\alpha {\mathbb Z}$ , through a $1$ -cocycle of G in ${\mathbb T}$ , with $\alpha $ commuting with the given dynamics. We first prove that any two such skew-product extensions are conjugate if and only if the corresponding cocycles are cohomologous. We then study unique ergodicity and unique ergodicity with respect to the fixed-point subalgebra by characterizing both in terms of the cocycle assigning the dynamics. The set of all invariant states is also determined: it is affinely homeomorphic with ${\mathcal P}({\mathbb T})$ , the Borel probability measures on the one-dimensional torus ${\mathbb T}$ , as long as the system is not uniquely ergodic. Finally, we show that unique ergodicity with respect to the fixed-point subalgebra of a skew-product extension amounts to the uniqueness of an invariant conditional expectation onto the fixed-point subalgebra.

Properties and examples of 𝐴-Landweber exact spectra

It is classically known that Landweber exact homology theories (complex oriented theories which are completely determined by complex cobordism) admit no nontrivial phantom maps. Herein we propose a definition of A A -Landweber exact spectra, for A A a compact abelian Lie group, and show that an analogous result on phantom maps holds. Also, we show that a conjecture of May on K U G KU_G is false. We do not prove an equivariant Landweber exact functor theorem, and therefore our result on phantom maps only applies to M U A MU_A , K U A KU_A , their p p -localizations, and B P A BP_A , which are shown to be A A -Landweber exact by ad-hoc methods.

Averaging multipliers on locally compact quantum groups

AbstractWe study an averaging procedure for completely bounded multipliers on a locally compact quantum group with respect to a compact quantum subgroup. As a consequence we show that central approximation properties of discrete quantum groups are equivalent to the corresponding approximation properties of their Drinfeld doubles. This is complemented by a discussion of the averaging of Fourier algebra elements. We compare the biinvariant Fourier algebra of the Drinfeld double of a discrete quantum group with the central Fourier algebra. In the unimodular case these are naturally identified, but we show by exhibiting a family of counter‐examples that they differ in general.

Strictly outer actions of locally compact groups: beyond the full factor case

Strictly outer actions of locally compact groups: beyond the full factor case

Mean Field Approaches to Lattice Gauge Theories: A Review

Due to their broad applicability, gauge theories (GTs) play a crucial role in various areas of physics, from high-energy physics to condensed matter. Their formulations on lattices, lattice gauge theories (LGTs), can be studied, among many other methods, with tools coming from statistical mechanics lattice models, such as mean field methods, which are often used to provide approximate results. Applying these methods to LGTs requires particular attention due to the intrinsic local nature of gauge symmetry, how it is reflected in the variables used to formulate the theory, and the breaking of gauge invariance when approximations are introduced. This issue has been addressed over the decades in the literature, yielding different conclusions depending on the formulation of the theory under consideration. In this article, we focus on the mean field theoretical approach to the analysis of GTs and LGTs, connecting both older and more recent results that, to the best of our knowledge, have not been compared in a pedagogical manner. After a brief overview of mean field theory in statistical mechanics and many-body systems, we examine its application to pure LGTs with a generic compact gauge group. Finally, we review the existing literature on the subject, discussing the results obtained so far and their dependence on the formulation of the theory.

Unimodular totally disconnected locally compact groups of rational discrete cohomological dimension one

Abstract It is shown that a Stallings–Swan theorem holds in a totally disconnected locally compact (= t.d.l.c.) context (cf. Theorem B). More precisely, a compactly generated $${\mathcal{C}\mathcal{O}}$$ C O -bounded t.d.l.c. group G of rational discrete cohomological dimension less than or equal to 1 must be isomorphic to the fundamental group of a finite graph of profinite groups. This result generalises Dunwoody’s rational version of the classical Stallings–Swan theorem to t.d.l.c. groups. The proof of Theorem B is based on the fact that a compactly generated unimodular t.d.l.c. group with rational discrete cohomological dimension 1 has necessarily non-positive Euler–Poincaré characteristic (cf. Theorem H).

On the existence of an extremal function for the Delsarte extremal problem

Abstract In the general setting of a locally compact Abelian group G, the Delsarte extremal problem asks for the supremum of integrals over the collection of continuous positive definite functions $$f \colon G \to \mathbb{R}$$ f : G → R satisfying $$f(0) = 1$$ f ( 0 ) = 1 and having $$supp f_{+} \subset \Omega$$ s u p p f + ⊂ Ω for some measurable subset $$\Omega$$ Ω of finite measure. In this paper, we consider the question of the existence of an extremal function for the Delsarte extremal problem. In particular, we show that there exists an extremal function for the Delsarte problem when $$\Omega$$ Ω is closed, extending previously known existence results to a larger class of functions.

One-form symmetries and the 3d $\mathcal{N}=2$ $A$-model: Topologically twisted indices and CS theories

We study three-dimensional \mathcal{N}=2𝒩=2 supersymmetric Chern–Simons-matter gauge theories with a one-form symmetry in the AA-model formalism on \Sigma_g× S^1Σg×S1. We explicitly compute expectation values of topological line operators that implement the one-form symmetry. This allows us to compute the topologically twisted index on the closed Riemann surface \Sigma_gΣg for any real compact gauge group GG as long as the ground states are all bosonic. All computations are carried out in the effective AA-model on \Sigma_gΣg, whose S^1S1 ground states are the so-called Bethe vacua. We discuss how the 3d one-form symmetry acts on the Bethe vacua, and also how its ’t Hooft anomaly constrains the vacuum structure. In the special case of the SU(N)_KSU(N)K\mathcal{N}=2𝒩=2 Chern–Simons theory, we obtain results for the (SU(N)/\mathbb{Z}_r)^{\theta}_K(SU(N)/ℤr)Kθ\mathcal{N}=2𝒩=2 Chern–Simons theories, for all non-anomalous \mathbb{Z}_r \subseteq \mathbb{Z}_Nℤr⊆ℤN subgroups of the centre of the gauge group, and with a \mathbb{Z}_rℤr\thetaθ-angle turned on. In the special cases with NN even, {N\over r} odd and {K\over r} even, we find a mixed ’t Hooft anomaly between gravity and the \mathbb{Z}_r^{(1)}ℤr(1) one-form symmetry of the SU(N)_KSU(N)K theory, and the infrared 3d TQFT after gauging is spin. In all cases, we count the Bethe states and the higher-genus states in terms of refinements of Jordan’s totient function. This counting gives us the twisted indices if and only if the infrared 3d TQFT is bosonic. Our results lead to precise conjectures about integrality of indices, which appear to have a strong number-theoretic flavour. Note: this paper directly builds upon unpublished notes by Brian Willett from 2020.

Unitary dual and matrix coefficients of compact nilpotent p-adic Lie groups with dimension $$d\le 5$$

Unitary dual and matrix coefficients of compact nilpotent p-adic Lie groups with dimension $$d\le 5$$

Projective representations of real semisimple Lie groups and the gradient map

Let G be a real noncompact semisimple connected Lie group and let ρ:G⟶SL(V) be a faithful irreducible representation on a finite-dimensional vector space V over R. We suppose that there exists a scalar product g on V such that ρ(G)=Kexp(p), where K=SO(V,g)∩ρ(G) and p=Symo(V,g)∩(dρ)e(g). Here, g denotes the Lie algebra of G, SO(V,g) denotes the connected component of the orthogonal group containing the identity element and Symo(V,g) denotes the set of symmetric endomorphisms of V with trace zero. In this paper, we study the projective representation of G on P(V) arising from ρ. There is a corresponding G-gradient map μp:P(V)⟶p. Using G-gradient map techniques, we prove that the unique compact G orbit O inside the unique compact UC orbit O′ in P(VC), where U is the semisimple connected compact Lie group with Lie algebra k⊕ip⊆sl(VC), is the set of fixed points of an anti-holomorphic involutive isometry of O′ and so a totally geodesic Lagrangian submanifold of O′. Moreover, O is contained in P(V). The restriction of the function μpβ(x):=⟨μp(x),β⟩, where ⟨·,·⟩ is an Ad(K)-invariant scalar product on p, to O achieves the maximum on the unique compact orbit of a suitable parabolic subgroup and this orbit is connected. We also describe the irreducible representations of parabolic subgroups of G in terms of the facial structure of the convex body given by the convex envelope of the image μp(P(V)).

TQFT gravity and ensemble holography

We outline a general derivation of holographic duality between “TQFT gravity” — the path integral of a 3d TQFT summed over different topologies — and an ensemble of boundary 2d CFTs. The key idea is to place the boundary ensemble on a Riemann surface of very high genus, where the duality trivializes. The duality relation at finite genus is then obtained by genus reduction. Our derivation is generic and does not rely on an explicit form of the bulk or boundary partition functions. It guarantees unitarity and suggests that the bulk sum should include all possible topologies. In the case of Abelian Chern-Simons theory with compact gauge group we argue that the weights of the boundary ensemble are equal, while the bulk sum reduces to a finite sum over equivalence classes of topologies, represented by handlebodies with possible line defects.

Locally compact groups with all dense subgroups separable

Abstract By a recent result of Juhász and van Mill, a locally compact topological group whose dense subspaces are all separable is metrizable. In this note we investigate the following question: Is every locally compact group having all dense subgroups separable also metrizable? We give an example to show the answer is negative for locally compact abelian groups, thereby showing that one cannot directly generalize the assertion by replacing “subspaces” with “subgroups”. On the other hand, we prove that the answer is positive for compact groups which are either connected or algebraically abelian; and for locally compact groups containing only separable subgroups. As an application, we obtain a necessary condition for metrizability of pronilpotent groups.

Index growth not imputable to topology

We employ partitioning methods, in the spirit of Montiel–Ros but here recast for general actions of compact Lie groups, to prove effective lower bounds on the Morse index of certain families of closed minimal hypersurfaces in the round four-dimensional sphere, and of free boundary minimal hypersurfaces in the Euclidean four-dimensional ball. Our analysis reveals, in particular, phenomena of linear index growth for sequences of minimal hypersurfaces of fixed topological type, in strong contrast to the three-dimensional scenario.

Semifinite von Neumann algebras in gauge theory and gravity

von Neumann algebras have been playing an increasingly important role in the context of gauge theories and gravity. The crossed product presents a natural method for implementing constraints through the commutation theorem, rendering it a useful tool for constructing gauge-invariant algebras. The crossed product of a Type III algebra with its modular automorphism group is semifinite, which means that the crossed product regulates divergences in local quantum field theories. In this article, we find a sufficient condition for the semifiniteness of the crossed product of a Type III algebra with locally compact group containing the modular automorphism group. Our condition surprisingly implies the centrality of the modular flow in the symmetry group, and we provide evidence for the necessity of this condition. Under these conditions, we construct an associated trace that computes physical expectation values. We comment on the importance of this result and its implications for subregion physics in gauge theory and gravity. Published by the American Physical Society 2025

About one group of metal magical objects in the Koban culture

This paper presents a review of Early Iron Age metal pellet bells found in archaeological contexts of Central and North Caucasus. Сonical pellet bells with openwork sound boxes belong to the exotic magical objects discovered in the burial complexes of the Koban culture. The main area of their distribution is the mountainous regions of the Central Caucasus, primarily the Koban necropolis. These objects form a rather homogeneous, compact group, differing mainly in the design of the “neck”, located between the cage and the loop. Pellet bells are mostly recovered in female burials, which are dated within the framework of the second half – end of the 8th century BC. They were part of amulet assemblages that formed necklaces and were used as charms associated with cosmogonic beliefs, animal cults and spell magic. The appearance of these objects should be considered as a result of borrowing (“import”) of ideas by the population of the Koban culture from the inhabitants of the South Caucasus, where various conical bellshaped pendants and pellet bells were well known in the Late Bronze-Early Iron Age. Cast in copper-alloy with a high amount of antimony, they show frequency-ranges from 0.2 kHz up to 20 kHz with noise character and rather low loudness.