Discrete conduche fibrations and C∗-algebras

Jonathan H. Brown; David N. Yetter

doi:10.1216/RMJ-2017-47-3-711

Discrete conduche fibrations and C∗-algebras

Jonathan H. Brown
, David N. Yetter

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

2 Scopus citations

Abstract

The k-graphs in the sense of Kumjian and Pask [7] are discrete Conduche fibrations over the monoid N^k, satisfying a finiteness condition. We examine the generalization of this construction to discrete Conduche fibrations with the same finiteness condition and a lifting property for completions of cospans to commutative squares, over any category satisfying a strong version of the right Ore condition, including all categories with pullbacks and right Ore categories in which all morphisms are monic.

Original language	English
Pages (from-to)	711-756
Number of pages	46
Journal	Rocky Mountain Journal of Mathematics
Volume	47
Issue number	3
DOIs	https://doi.org/10.1216/RMJ-2017-47-3-711
State	Published - 1 Jan 2017
Externally published	Yes

Keywords

Conduché fibrations
Cuntz-Krieger algebra
Groupoids

ASJC Scopus subject areas

General Mathematics

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10.1216/RMJ-2017-47-3-711

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abstract = "The k-graphs in the sense of Kumjian and Pask [7] are discrete Conduche fibrations over the monoid Nk, satisfying a finiteness condition. We examine the generalization of this construction to discrete Conduche fibrations with the same finiteness condition and a lifting property for completions of cospans to commutative squares, over any category satisfying a strong version of the right Ore condition, including all categories with pullbacks and right Ore categories in which all morphisms are monic.",

keywords = "Conduch{\'e} fibrations, Cuntz-Krieger algebra, Groupoids",

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AB - The k-graphs in the sense of Kumjian and Pask [7] are discrete Conduche fibrations over the monoid Nk, satisfying a finiteness condition. We examine the generalization of this construction to discrete Conduche fibrations with the same finiteness condition and a lifting property for completions of cospans to commutative squares, over any category satisfying a strong version of the right Ore condition, including all categories with pullbacks and right Ore categories in which all morphisms are monic.

KW - Conduché fibrations

KW - Cuntz-Krieger algebra

KW - Groupoids

UR - https://www.scopus.com/pages/publications/85021266071

U2 - 10.1216/RMJ-2017-47-3-711

DO - 10.1216/RMJ-2017-47-3-711

M3 - Article

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EP - 756

JO - Rocky Mountain Journal of Mathematics

JF - Rocky Mountain Journal of Mathematics

IS - 3

ER -

Discrete conduche fibrations and C∗-algebras

Abstract

Keywords

ASJC Scopus subject areas

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