A new approach to recent constructions of C*-algebras from modular index theory

TL;DR

This paper introduces a new perspective on C*-algebras from modular index theory, showing they can be viewed as corners of semigroup C*-algebras, enabling systematic analysis.

Contribution

It provides a novel identification of recent C*-algebra constructions with corners in semigroup C*-algebras, facilitating deeper structural understanding.

Findings

Identification of C*-algebras with corners in semigroup C*-algebras

Analysis of canonical maximal abelian subalgebras

Systematic approach to these algebraic structures

Abstract

We present a new approach to C*-algebras recently constructed in the context of modular index theory by Carey, Phillips, Putnam and Rennie. It turns out that their constructions can be identified with full corners of ideals in semigroup C*-algebras. This new point of view leads to a systematic analysis of these algebras and their canonical maximal abelian subalgebras.