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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.09015 |
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| _version_ | 1866916652131549184 |
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| author | Duah, Zachary Preez, Stian Du Milan, David Ramamurthy, Shreyas Vega, Lucas |
| author_facet | Duah, Zachary Preez, Stian Du Milan, David Ramamurthy, Shreyas Vega, Lucas |
| contents | We investigate the use of labelled graphs as a Morita equivalence invariant for inverse semigroups. We construct a labelled graph from a combinatorial inverse semigroup $S$ with $0$ admitting a special set of idempotent $\mathcal{D}$-class representatives and show that $S$ is Morita equivalent to a labelled graph inverse semigroup. For the inverse hull $S$ of a Markov shift, we show that the labelled graph determines the Morita equivalence class of $S$ among all other inverse hulls of Markov shifts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_09015 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Labelled graphs as Morita equivalence invariants for a class of inverse semigroups Duah, Zachary Preez, Stian Du Milan, David Ramamurthy, Shreyas Vega, Lucas Group Theory 20M18 We investigate the use of labelled graphs as a Morita equivalence invariant for inverse semigroups. We construct a labelled graph from a combinatorial inverse semigroup $S$ with $0$ admitting a special set of idempotent $\mathcal{D}$-class representatives and show that $S$ is Morita equivalent to a labelled graph inverse semigroup. For the inverse hull $S$ of a Markov shift, we show that the labelled graph determines the Morita equivalence class of $S$ among all other inverse hulls of Markov shifts. |
| title | Labelled graphs as Morita equivalence invariants for a class of inverse semigroups |
| topic | Group Theory 20M18 |
| url | https://arxiv.org/abs/2411.09015 |