2026-05-20T05:00:57Zhttps://keep.lib.asu.edu/oai/requestoai:keep.lib.asu.edu:node-1294492025-05-20T15:17:28Zoai_pmh:alloai_pmh:repo_items129449
https://hdl.handle.net/2286/R.I.27935
<p>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</p>
10.1090/S0002-9947-2014-06008-X
1088-6850
0002-9947
http://rightsstatements.org/vocab/InC/1.0/
2014-11-01
37 pages
eng
Spielberg, John
College of Liberal Arts and Sciences
This is the author's final accepted manuscript. The final version was first published in TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY in 366 (2014), published by the American Mathematical Society at http://dx.doi.org/10.1090/S0002-9947-2014-06008-X
<p>In this paper we describe a new method of defining C<sup>*</sup>-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<sup>*</sup>-algebras, and for aperiodicity, which is used to prove the standard uniqueness theorems.</p>
Text
Groupoids and C*-Algebras for Categories of Paths