C*-algebras generated by cancellative semigroups

Abstract

A C * -algebra generated by a commuting family of isometries is a natural generalization of the Toeplitz algebra. We study the * -automorphisms and invariant ideals of the C * -algebra generated by a semigroup.

The structure of C*-subalgebras of the Toeplitz algebra fixed with respect to a finite group of automorphisms

“…In [5,6] it is shown that the mapping A → A, A = A(1), generates an isomorphism between the C * -algebras T and T . Analogous results for a more general case were obtained in [7]. Thus, the representation σ :…”

Nets of graded $C^*$-algebras over partially ordered sets

“…We have studied earlier the C * -algebras generated by representations of ordered semigroups [7,8,9,10,11,12]. The present paper is a continuation of the study begun in the article [13].…”

On isometric representations of the perforated semigroup

“…We say that the isometric representation π : S → B(H π ) is an inverse representation if S * π is an inverse semigroup under the operation of *involution, or equialently, the semigroup S * 0,π is a semigroup of idempotents in S * π , that is, the semigroup of orthogonal projections. According to the Lemma 2.2 in [5] every semigroup S has at least one inverse representation. On the other hand if the defined above order on S is a total order, then all the isometric representations of the semigroup S are inverse (see [1]).…”