Structure of the Group of Automorphisms of C-algebras
نویسنده
چکیده
We obtain a kind of structure theorem for the automorphism group AutA of a unital C-algebra A. According to it, AutA can be regarded as a subgroup of the semi-direct product of direct product group consisting of some family of projective unitary groups and some permutation group on the spectrum of A.
منابع مشابه
A K-Theoritic Approach to Some C*-Algebras
In this paper we look at the K-theory of a specific C*-algebra closely related to the irrational rotation algebra. Also it is shown that any automorphism of a C*-algebra A induces group automorphisms of K_{1}(A) amd K_{0}(A) in an obvious way. An interesting problem for any C*-algebra A is to find out whether, given an automorphism of K_{0}(A) and an automorphism of K_{1}(A), we can lift them t...
متن کاملALGEBRAS WITH CYCLE-FINITE STRONGLY SIMPLY CONNECTED GALOIS COVERINGS
Let $A$ be a nite dimensional $k-$algebra and $R$ be a locally bounded category such that $R rightarrow R/G = A$ is a Galois covering dened by the action of a torsion-free group of automorphisms of $R$. Following [30], we provide criteria on the convex subcategories of a strongly simply connected category R in order to be a cycle- nite category and describe the module category of $A$. We p...
متن کاملNon-commutative Entropy Computations for continuous fields and cross-products
We present here two non-commutative situations where dynamical entropy estimates are possible. The first result is concerned with automorphisms of cross-products by an exact group that commute with the group action and generalizes the result known for amenable group. The second is about continuous fields of C∗-algebras and C(X)automorphisms and shows that one need more than the knowledge of ent...
متن کاملTopological Entropy of Some Automorphisms of Reduced Amalgamated Free Product C–algebras
Certain classes of automorphisms of reduced amalgamated free products of C∗– algebras are shown to have Brown–Voiculescu topological entropy zero. Also, for automorphisms of exact C∗–algebras, the Connes–Narnhofer–Thirring entropy is shown to be bounded above by the Brown–Voiculescu entropy. These facts are applied to generalize Størmer’s result about the entropy of automorphisms of the II1–fac...
متن کاملOn Marginal Automorphisms of a Group Fixing the Certain Subgroup
Let W be a variety of groups defined by a set W of laws and G be a finite p-group in W. The automorphism α of a group G is said to bea marginal automorphism (with respect to W), if for all x ∈ G, x−1α(x) ∈ W∗(G), where W∗(G) is the marginal subgroup of G. Let M,N be two normalsubgroups of G. By AutM(G), we mean the subgroup of Aut(G) consistingof all automorphisms which centralize G/M. AutN(G) ...
متن کاملPrimitive Ideal Space of Ultragraph $C^*$-algebras
In this paper, we describe the primitive ideal space of the $C^*$-algebra $C^*(mathcal G)$ associated to the ultragraph $mathcal{G}$. We investigate the structure of the closed ideals of the quotient ultragraph $ C^* $-algebra $C^*left(mathcal G/(H,S)right)$ which contain no nonzero set projections and then we characterize all non gauge-invariant primitive ideals. Our results generalize the ...
متن کامل