The universal Boolean inverse semigroup presented by the abstract Cuntz-Krieger relations
Operator Algebras
2019-03-01 v3
Abstract
This paper is a contribution to the theory of what might be termed -dimensional non-commutative spaces. We prove that associated with each inverse semigroup is a Boolean inverse semigroup presented by the abstract versions of the Cuntz-Krieger relations. We call this Boolean inverse semigroup the Exel completion of and show that it arises from Exel's tight groupoid under non-commutative Stone duality.
Cite
@article{arxiv.1902.02583,
title = {The universal Boolean inverse semigroup presented by the abstract Cuntz-Krieger relations},
author = {Mark V Lawson and Alina Vdovina},
journal= {arXiv preprint arXiv:1902.02583},
year = {2019}
}
Comments
This revised version of the paper contains a genearalization suggested by Enrique Pardo (using a result of Lisa Orloff Clark) and answers some questions posed by Ruy Exel