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arXiv · 2411.09015

Labelled graphs as Morita equivalence invariants for a class of inverse semigroups

Zachary Duah·Stian Du Preez·David Milan·Shreyas Ramamurthy·Lucas Vega
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Abstract

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.

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Zachary Duah, Stian Du Preez, David Milan, Shreyas Ramamurthy, Lucas Vega. 2024-11-13. Labelled graphs as Morita equivalence invariants for a class of inverse semigroups. https://arxiv.org/abs/2411.09015

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