JOINS AND COVERS IN INVERSE SEMIGROUPS AND TIGHT C*-ALGEBRAS

Authors

Allan P. Donsig, University of Nebraska-LincolnFollow
David Milan, University of Texas at Tyler

Document Type

Article

Date of this Version

2013

Citation

Bull. Aust. Math. Soc. 90 (2014), 121–133; doi:10.1017/S0004972713001111

Comments

Copyright © 2014 Australian Mathematical Publishing Association Inc. Used by permission.

Abstract

We show Exel’s tight representation of an inverse semigroup can be described in terms of joins and covers in the natural partial order. Using this, we show that the C*-algebra of a finitely aligned category of paths, developed by Spielberg, is the tight C*-algebra of a natural inverse semigroup. This includes as a special case finitely aligned higher-rank graphs: that is, for such a higher-rank graph Ʌ, the tight C* -algebra of the inverse semigroup associated to Ʌ is the same as the C*-algebra of Ʌ.