FINITELY PRESENTED INVERSE SEMIGROUPS WITH FINITELY MANY IDEMPOTENTS IN EACH <i>D</i> -CLASS AND NON-HAUSDORFF UNIVERSAL GROUPOIDS

• Type: Article in International Scientific Journal
• Date: 2024

Authors

Pedro V. Silva (Author) FCUP; Steinberg, B (Author) Other

Journal

Title: Journal of the Australian Mathematical Society

Vol. 116

Pages: 384-398

ISSN: 1446-7887

Publisher: Cambridge University Press

Indexing

ISI Web of Knowledge - 0 Citations

Scopus - 0 Citations

Other information

Authenticus ID: P-00Z-J1J

DOI: 10.1017/s1446788723000198

Abstract (EN): The complex algebra of an inverse semigroup with finitely many idempotents in each D -class is stably finite by a result of Munn. This can be proved fairly easily using C* -algebras for inverse semigroups satisfying this condition that have a Hausdorff universal groupoid, or more generally for direct limits of inverse semigroups satisfying this condition and having Hausdorff universal groupoids. It is not difficult to see that a finitely presented inverse semigroup with a non-Hausdorff universal groupoid cannot be a direct limit of inverse semigroups with Hausdorff universal groupoids. We construct here countably many nonisomorphic finitely presented inverse semigroups with finitely many idempotents in each D -class and non-Hausdorff universal groupoids. At this time, there is not a clear C* -algebraic technique to prove these inverse semigroups have stably finite complex algebras.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 15