Toeplitz algebras associated to Endomorphisms of Ore semigroups

Abstract

In this paper, we consider the Toeplitz algebra associated to actions of Ore semigroups on $C^{\ast }$-algebras. In particular, we consider injective and surjective actions of such semigroups. We use the theory of groupoid dynamical systems to represent the Toeplitz algebra as a groupoid crossed product. We also discuss the K-theory of the Toeplitz algebra in some examples. For instance, we show that for the semigroup of positive matrices, the K-theory of the associated Toeplitz algebra vanishes.

References in corpus (2)

• Renault's Equivalence Theorem for Groupoid Crossed Products
• An equivalence theorem for reduced Fell bundle C*-algebras

Cited by in corpus (1)

• On the Wiener-Hopf compactification of a Symmetric Cone