Automorphism Groups Of Algebras Research Articles

The automorphism groups of the vertex operator algebras V+L: general case

In this article, we give a method of calculating the automorphism groups of the vertex operator algebras V + L associated with even lattices L. For example, by using this method we determine the automorphism groups of V + L for even lattices of rank one, two and three, and even unimodular lattices.

Weak Hopf algebras corresponding to Cartan matrices

We replace the group of grouplike elements of the quantized enveloping algebra Uq(g) of a finite dimensional semisimple Lie algebra g by some regular monoid and get the weak Hopf algebra wqd(g). It is a subclass of weak Hopf algebras but not Hopf algebras. Then we devote to constructing a basis of wqd(g) and determine the group of weak Hopf algebra automorphisms of wqd(g) when q is not a root of unity.

ANDERSÉN–LEMPERT-THEORY WITH PARAMETERS: A REPRESENTATION THEORETIC POINT OF VIEW

We calculate the invariant subspaces in the linear representation of the group of algebraic automorphisms of ℂnon the vector space of algebraic vector fields on ℂnand more generally we do this in a setting with parameter. As an application to the field of Several Complex Variables we get a new proof of the Andersén–Lempert observation and a parametric version of the Andersén–Lempert theorem. Further applications to the question of embeddings of ℂkinto ℂnare announced.

On intertwining operators and finite automorphism groups of vertex operator algebras

Let V be a simple vertex operator algebra and G a finite automorphism group. We give a construction of intertwining operators for irreducible V G -modules which occur as submodules of irreducible V-modules by using intertwining operators for V. We also determine some fusion rules for a vertex operator algebra as an application.

Sur la structure du groupe d’automorphismes de certaines surfaces affines

We describe the structure of the group of algebraic automorphisms of the following surfaces 1) P1 k ×P1 k minus a diagonal; 2) P1 k ×P 1 k minus a fiber. The motivation is to get a new proof of two theorems proven respectively by L. Makar-Limanov and H. Nagao. We also discuss the structure of the semi-group of polynomial proper maps from C2 to C2.

Automorphisms of radical W-type non-associative algebras I

We define the non-associative algebra N(Irr(F[x], n,σ)) which is simple and Lie admissible [6]. There is a class C of subalgebras of N(Irr(F[x], n,σ)) such that each nonassociative algebra automorphism group of an algebra in C is trivial.

Automorphism groups of finite dimensional simple algebras

We show that if a field k contains sufficiently many elements (for instance, if k is infinite), and K is an algebraically closed field containing k, then every linear algebraic k-group over K is k-isomorphic to Aut(A ⊗k K), where A is a finite dimensional simple algebra over k. In this paper, ‘algebra’ over a field means ‘nonassociative algebra’, i.e., av ector space A over this field with multiplication given by a linear map A ⊗ A → A, a1 ⊗ a2 � a1a2, subject to no a priori conditions; cf. [Sc]. Fix a field k and an algebraically closed field extension K/k. Our point of view of algebraic groups is that of [Bor], [H], [Sp]; the underlying varieties of linear algebraic groups will be the affine algebraic varieties over K .A susual, algebraic group (resp., subgroup, homomorphism) defined over k is abbreviated to k-group (resp., k-subgroup, k-homomorphism). If E/F is a field extension and V is a vector space over F ,w edenote by VE the vector space V ⊗F E over E. Let A be a finite dimensional algebra over k and let V be its underlying vector space. The k-structure V on VK defines the k-structure on the linear algebraic group GL(VK). As Aut(AK), the full automorphism group of AK, is a closed subgroup of GL(VK), it has the structure of a linear algebraic group. If Aut(AK )i sdefined over k (that is always the case if k is perfect; cf. [Sp, 12.1.2]), then for each field extension F/k the full automorphism group Aut(AF )o fF -algebra AF is the group Aut(AK)(F )o fF -rational points of the algebraic group Aut(AK).

The Coradical Filtration for Drinfeld Double Ringel-Hall Algebras

Let 𝒟(Λ) be the Drinfeld double Ringel-Hall algebra with Λ being any finite dimensional hereditary algebra over a finite field k. We determine the coradical filtration for 𝒟(Λ). As an application, we describe the group of Hopf algebra automorphisms of the Drinfeld double Ringel composition algebra of Λ.

Polyhedral K 2

Using elementary graded automorphisms of polytopal algebras (essentially the coordinate rings of projective toric varieties) polyhedral versions of the group of elementary matrices and the Steinberg and Milnor groups are defined. They coincide with the usual K-theoretic groups in the special case when the polytope is a unit simplex and can be thought of as compact/polytopal substitutes for the tame automorphism groups of polynomial algebras. Relative to the classical case, many new aspects have to be taken into account. We describe these groups explicitly when the underlying polytope is 2-dimensional. Already this low-dimensional case provides interesting classes of groups.

On isometries of some Riemannian Lie groups

We study isometry groups of Lie groups endowed with left-invariant Riemannian metrics. We mainly consider triangular Lie groups. By the familiar Gordon-Wilson theorem, calculating the isometry groups of left-invariant metrics on such groups is reduced to calculating the automorphism groups of the corresponding Lie algebras and to distinguishing compact subgroups of these groups. We consider nilpotent Lie groups in more detail, with special attention to filiform Lie groups and their relatives (prefiliform, quasifiliform). As a rule, we state the main results in terms of the automorphism groups of Lie algebras and then give their geometric interpretation. Special attention is paid to finding the group of connected components of the isometry group (in particular, it is calculated for all filiform Lie groups) and to conditions guaranteeing that the group of rotations (that is, isometries preserving a given point) is finite for certain classes of Riemannian Lie groups.

Isomorphism classes and automorphism groups of algebras of Weyl type

Abstract In one of our recent papers, the associative and the Lie algebras of Weyl type A[D]=A F[D] were defined and studied, where A is a commutative associative algebra with an identity element over a field F of any characteristic, and F[D] is the polynomial algebra of a commutative derivation subalgebra D of A. In the present paper, a class of the above associative and Lie algebras A[D] with F being a field of characteristic 0, D consisting of locally finite but not locally nilpotent derivations of A, are studied.The isomorphism classes and automorphism groups of these associative and Lie algebras are determined.

Automorphism groups of Weyl-type algebras

Let F be a field of characteristic 0, be n commuting variables over F, and be the field of all rational functions. Let . We have the simple Weyl type algebra . In this paper, the automorphism group of the associative algebra and the automorphism group of the Lie algebra are determined, and it is proved that .

Polytopal linear retractions

We investigate graded retracts of polytopal algebras (essentially the homogeneous rings of affine cones over projective toric varieties) as polytopal analogues of vector spaces. In many cases we show that these retracts are again polytopal algebras and that codimension 1 1 retractions factor through retractions preserving the semigroup structure. We expect that these results hold in general. This paper is a part of the project started by the authors in 1999, where we investigate the graded automorphism groups of polytopal algebras. Part of the motivation comes from the observation that there is a reasonable ‘polytopal’ generalization of linear algebra (and, subsequently, that of algebraic K K -theory).

Indices of Toeplitz tuples on pseudoregular domains

This paper proves an index theorem of Toeplitz tuples on pseudoregular domains in Cn. Geometrically, the index of Toeplitz tupleT n is (-1) n time wrapping number of φ n around the origin. As one of the applications of the index theorem, we completely characterize the automorphism groups of Toeplitz algebras on Poincare domain. As another application, it is shown thatC*(Ω)≅C*(Bn) for every Poincare domain Ω inC n (n≠2). It is also noticed thatC*(Ω)≅C*(B 2) if and only if the Poincare conjecture is true for ∂Ω.

Locally representable one-parameter automorphism groups of AF algebras and KMS states

As a mathematical model of classical statistical lattice systems we consider locally representable one-parameter automorphism groups of AF (approximately finite-dimensional) C ∗- algebras . We demonstrate how to construct examples which exhibit various types of non uniqueness of equilibrium states (or KMS states). Towards the classification problem of cocycle-conjugacy classes of one-parameter automorphism groups in general we introduce a new invariant called marginal spectrum (associated with ground states) and apply it to a special case of infinite tensor product type actions.

The Coradical Filtration for Quantized Enveloping Algebras

We determine the coradical filtration on a quantized enveloping algebra t/9(g) = U defined over Q(q). As applications, we determine the biideals of U and describe the group of Hopf algebra automorphisms of U.

The coradical filtration of U q(g)at roots of unity

We compute the coradical filtration and the group of Hopf algebra automorphisms of the non-restricted specialization of the quantized universal enveloping algebra of a finite-dimensional semisimple Lie algebra.

Structure of weak automorphism groups of mono-unary algebras

A weak automorphism of an algebra on A with the set T of term operations is a permutation of $\tau$ of A such that $\tau^{-1}T\tau=T$ . In this note we describe the groups of weak automorphisms of mono-unary algebras. Some examples of such algebras without weak automorphisms are given.

On voa associated with special jordan algebras

For a given simple Jordan algebra A of type A, B or C over C, we construct a vertex operator algebra V such that the weight two space V 2 ≅ A by using the structure of Heisenberg algebras. In addition, we compute the automorphism groups of these vertex operator algebras.

On the automorphism groups of rational group algebras of metacyclic groups

On the automorphism groups of rational group algebras of metacyclic groups