On zigzag maps and the path category of an inverse semigroup
Group Theory
2018-11-13 v1 Operator Algebras
Abstract
We study the path category of an inverse semigroup admitting unique maximal idempotents and give an abstract characterization of the inverse semigroups arising from zigzag maps on a left cancellative category. As applications we show that every inverse semigroup is Morita equivalent to an inverse semigroup of zigzag maps and hence the class of Cuntz-Krieger -algebras of singly aligned categories include the tight -algebras of all countable inverse semigroups, up to Morita equivalence.
Keywords
Cite
@article{arxiv.1811.04124,
title = {On zigzag maps and the path category of an inverse semigroup},
author = {Allan Donsig and Jennifer Gensler and Hannah King and David Milan and Ronen Wdowinski},
journal= {arXiv preprint arXiv:1811.04124},
year = {2018}
}