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arXiv · 2206.11999

Quantum Inverse Semigroups

Marcelo Muniz Alves·Eliezer Batista·Francielle Kuerten Boeing
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Abstract

In this work, the notion of a quantum inverse semigroup is introduced as a linearized generalization of inverse semigroups. Beyond the algebra of an inverse semigroup, which is the natural example of a quantum inverse semigroup, several other examples of this new structure are presented in different contexts, those are related to Hopf algebras, weak Hopf algebras, partial actions and Hopf categories. Finally, a generalized notion of local bisections are defined for commutative Hopf algebroids over a commutative base algebra giving rise to new examples of quantum inverse semigroups associated to Hopf algebroids in the same sense that inverse semigroups are related to groupoids.

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BibTeXRIS

Marcelo Muniz Alves, Eliezer Batista, Francielle Kuerten Boeing. 2022-06-23. Quantum Inverse Semigroups. https://arxiv.org/abs/2206.11999

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