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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.
- Spielberg, John (Author)
- College of Liberal Arts and Sciences (Contributor)
Spielberg, Jack (2014). GROUPOIDS AND C*-ALGEBRAS FOR CATEGORIES OF PATHS. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 366(11), 5771-5819. http://dx.doi.org/10.1090/S0002-9947-2014-06008-X
- 2015-02-17 12:00:21
- 2021-11-05 01:14:53
- 3 years ago