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Corrigendum to "A New Uniqueness Theorem for the Tight C*-algebra of an Inverse Semigroup" [C. R. Math. Acad. Sci. Soc. R. Can. 44 (2022), no. 4, 88--112]

Chris Bruce, Charles Starling

Abstract

We correct the proof of Theorem 4.1 from [C. R. Math. Acad. Sci. Soc. R. Can. \textbf{44} (2022), no. 4, 88--112].

Corrigendum to "A New Uniqueness Theorem for the Tight C*-algebra of an Inverse Semigroup" [C. R. Math. Acad. Sci. Soc. R. Can. 44 (2022), no. 4, 88--112]

Abstract

We correct the proof of Theorem 4.1 from [C. R. Math. Acad. Sci. Soc. R. Can. \textbf{44} (2022), no. 4, 88--112].
Paper Structure (2 sections, 1 theorem, 10 equations)

This paper contains 2 sections, 1 theorem, 10 equations.

Table of Contents

  1. Introduction
  2. The proof of St22

Key Result

Theorem 2.1

Let $P$ be a right LCM monoid and $S$ the associated inverse semigroup as in StLCM, let $\mathcal{Q}_r(P)= C^*_r(\mathcal{G}_{\text{tight}}(S))$ denote its reduced boundary quotient C*-algebra, and let $\mathcal{Q}_{r,c}(P) = C^*(T_{[p,q]}: p,q\in P_c)\subseteq \mathcal{Q}_r(P)$ be the C*-subalgebra

Theorems & Definitions (2)

  • Theorem 2.1
  • proof