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GROUPOIDS AND C*-ALGEBRAS FOR CATEGORIES OF PATHS.
- Source :
- Transactions of the American Mathematical Society; Nov2014, Vol. 366 Issue 11, p5771-5819, 49p
- Publication Year :
- 2014
-
Abstract
- In this paper we describe a new method of defining C*-algebras from oriented combinatorial data, thereby generalizing the construction of algebras from directed graphs, higher-rank graphs, and ordered groups. We show that only the most elementary notions of concatenation and cancellation of paths are required to define versions of Cuntz-Krieger and Toeplitz-Cuntz- Krieger algebras, and the presentation by generators and relations follows naturally. We give sufficient conditions for the existence of an AF core, hence of the nuclearity of the C*-algebras, and for aperiodicity, which is used to prove the standard uniqueness theorems. [ABSTRACT FROM AUTHOR]
- Subjects :
- GROUPOIDS
LINEAR operators
ALGEBRA
TOEPLITZ operators
GRAPH theory
Subjects
Details
- Language :
- English
- ISSN :
- 00029947
- Volume :
- 366
- Issue :
- 11
- Database :
- Complementary Index
- Journal :
- Transactions of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 98062090
- Full Text :
- https://doi.org/10.1090/S0002-9947-2014-06008-X