FINITELY PRESENTED INVERSE SEMIGROUPS WITH FINITELY MANY IDEMPOTENTS IN EACH -CLASS AND NON-HAUSDORFF UNIVERSAL GROUPOIDS
Abstract The complex algebra of an inverse semigroup with finitely many idempotents in each $\mathcal D$ -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...
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| Published in: | Journal of the Australian Mathematical Society (2001) 2024-06, Vol.116 (3), p.1-15 |
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| Main Authors: | , |
| Format: | Article |
| Language: | eng |
| Subjects: | |
| Online Access: | Get full text |
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| Summary: | Abstract The complex algebra of an inverse semigroup with finitely many idempotents in each $\mathcal D$ -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 $\mathcal D$ -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. |
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| ISSN: | 1446-7887 1446-8107 |