Quantum Inverse Semigroups

• Main Authors: Alves, Marcelo Muniz, Batista, Eliezer, Boeing, Francielle Kuerten
• Format: Journal Article
• Language: English
• Published: 23-06-2022
• Subjects: Mathematics - Quantum Algebra; Mathematics - Rings and Algebras
• DOI: 10.48550/arxiv.2206.11999

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.