Quantum inverse semigroups

  • Marcelo Muniz Alves

    Universidade Federal do Paraná, Curitiba-PR, Brazil
  • Eliezer Batista

    Universidade Federal de Santa Catarina, Florianópolis-SC, Brazil
  • Francielle Kuerten Boeing

    Universidade Federal de Santa Catarina, Florianópolis-SC, Brazil
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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 is defined for commutative Hopf algebroids over a commutative base algebra giving rise to new examples of quantum inverse semigroups associated with Hopf algebroids in the same sense that inverse semigroups are related to groupoids.

Cite this article

Marcelo Muniz Alves, Eliezer Batista, Francielle Kuerten Boeing, Quantum inverse semigroups. J. Noncommut. Geom. 18 (2024), no. 2, pp. 681–739

DOI 10.4171/JNCG/540