Groupoids and C∗-algebras for left cancellative small categories

Jack Spielberg

doi:10.1512/iumj.2020.69.7969

Groupoids and C^∗-algebras for left cancellative small categories

Jack Spielberg

Mathematical and Statistical Sciences, School of (SoMSS)

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

Categories of paths are a generalization of several kinds of oriented discrete data that have been used to construct C^∗-algebras. The techniques introduced to study these constructions apply almost verbatim to the more general situation of left cancellative small categories. We develop this theory and derive the structure of the C^∗-algebras in the most general situation. We analyze the regular representation, and the Wiener-Hopf algebra in the case of a subcategory of a groupoid.

Original language	English (US)
Pages (from-to)	1579-1626
Number of pages	48
Journal	Indiana University Mathematics Journal
Volume	69
Issue number	5
DOIs	https://doi.org/10.1512/iumj.2020.69.7969
State	Published - 2020

Keywords

Cuntz-Krieger algebras
Groupoids
Left cancellative small categories
Monoids
Toeplitz algebras
Weiner-Hopf algebras

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1512/iumj.2020.69.7969

Cite this

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title = "Groupoids and C∗-algebras for left cancellative small categories",

abstract = "Categories of paths are a generalization of several kinds of oriented discrete data that have been used to construct C∗-algebras. The techniques introduced to study these constructions apply almost verbatim to the more general situation of left cancellative small categories. We develop this theory and derive the structure of the C∗-algebras in the most general situation. We analyze the regular representation, and the Wiener-Hopf algebra in the case of a subcategory of a groupoid.",

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KW - Monoids

KW - Toeplitz algebras

KW - Weiner-Hopf algebras

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