Quantum inverse semigroups
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...
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| Published in: | Journal of noncommutative geometry Vol. 18; no. 2; pp. 681 - 739 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
01-01-2024
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| Online Access: | Get full text |
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| Summary: | 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. |
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| ISSN: | 1661-6952 1661-6960 |
| DOI: | 10.4171/jncg/540 |