Groupoids and $C^*$-algebras for left cancellative small categories
Operator Algebras
2018-06-13 v2
Abstract
Categories of paths are a generalization of several kinds of oriented discrete data that have been used to construct -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 -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.
Keywords
Cite
@article{arxiv.1712.07720,
title = {Groupoids and $C^*$-algebras for left cancellative small categories},
author = {Jack Spielberg},
journal= {arXiv preprint arXiv:1712.07720},
year = {2018}
}
Comments
30 pages. Various small corrections, and one substantive: the previous Cuntz-Krieger condition was incorrect. Definition 10.8 and Theorem 10.10 have been modified To appear in Indiana University Mathematics Journal