The Brauer group of graded continuous trace $C\sp *$-algebras

Brauer Algebras and the Brauer Group

An algebra is a vector space V over a field k together with a kbilinear product of vectors under which V is a ring. A certain class of algebras, called Brauer algebras algebras which split over a finite Galois extension appear in many subfields of abstract algebra, including K-theory and class field theory. Beginning with a definition of the the tensor product, we define and study Brauer algebr...

The symmetric group and Brauer algebras

Complex Group Algebras of Finite Groups : Brauer ’ S Problem 1

Brauer’s Problem 1 asks the following: what are the possible complex group algebras of finite groups? It seems that with the present knowledge of representation theory it is not possible to settle this question. The goal of this paper is to announce a partial solution to this problem. We conjecture that if the complex group algebra of a finite group does not have more than a fixed number m of i...

On Amenability of Group Algebras, Ii: Graded Algebras

We show that, in a finitely generated amenable group G with lower central series (γn(G)), the function n 7→ rank(γn(G)/γn+1(G)) grows subexponentially. This paper continues [22,2]’s study of amenability of affine algebras (based on the notion of almost-invariant finite-dimensional subspace), and applies it to graded algebras associated with finitely generated groups. We consider the graded defo...

Endomorphisms of stable continuous-trace C-algebras

We classify spectrum-preserving endomorphisms of stable continuoustrace C∗-algebras up to inner automorphism by a surjective multiplicative invariant taking values in finite dimensional vector bundles over the spectrum. Specializing to automorphisms, this gives a different approach to results of Phillips and Raeburn. 2000 Mathematics Subject Classification: 46L05, 46M20