Toeplitz algebras associated to Endomorphisms of Ore semigroups

2015/03/03 by S. Sundar, Sundar, S. · 1 citation
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Geometric and Algebraic Topology #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1503.00828

openalex publication_date 2015/03/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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• Reduced C^*-algebras of Product Systems -- an E₀-semigroup and a Groupoid perspective

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