Toeplitz algebras associated to Endomorphisms of Ore semigroups

TL;DR

This paper studies Toeplitz algebras arising from Ore semigroup actions on C*-algebras, using groupoid dynamical systems to analyze their structure and K-theory, with specific examples like positive matrices.

Contribution

It introduces a groupoid approach to Toeplitz algebras for Ore semigroup actions and explores their K-theory in concrete cases.

Findings

Toeplitz algebra represented as a groupoid crossed product

K-theory of the Toeplitz algebra can vanish in specific examples

Analysis of injective and surjective semigroup actions

Abstract

In this paper, we consider the Toeplitz algebra associated to actions of Ore semigroups on $C^{*}$-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.