Quantum Inverse Semigroups
Quantum Algebra
2023-04-03 v2 Rings and Algebras
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.
Cite
@article{arxiv.2206.11999,
title = {Quantum Inverse Semigroups},
author = {Marcelo Muniz Alves and Eliezer Batista and Francielle Kuerten Boeing},
journal= {arXiv preprint arXiv:2206.11999},
year = {2023}
}
Comments
1 figure. Revised version