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LOCAL BISECTIONS OF HOPF ALGEBROIDS AND INVERSE SEMIGROUPS
- Speaker(s)
- ELIEZER BATISTA
- Affiliation
- Universidade Federal de Santa Catarina, Florianópolis, Brazil
- Language of the talk
- English
- Date
- June 4, 2025, 5:15 p.m.
- Information about the event
- IMPAN 405 & ZOOM
- Title in Polish
- LOCAL BISECTIONS OF HOPF ALGEBROIDS AND INVERSE SEMIGROUPS
- Seminar
- North Atlantic Noncommutative Geometry Seminar
The relationship between étale groupoids and inverse semigroups via local bisections has been known for a long time. In particular, there is an adjunction between the category of étale groupoids with morphisms defined from actions of one groupoid upon the other (algebraic morphisms) and the category of inverse semigroups with usual morphisms. On the one hand, there is a functor associating to any étale groupoid the inverse semigroup of its local bisections. On the other hand, there is a functor defined by the germ groupoid of actions of the inverse semigroup on the space of characteristic functions of its set of idempotents. Our aim is to establish the same kind of equivalence between commutative Hopf algebroids and inverse semigroups. One direction is totally complete, we constructed the inverse semigroup of local biretractions of a commutative Hopf algebroid. (We use the term "biretraction" because the arrows go in the opposite direction than in the case of groupoids.) Also, we defined a category of commutative Hopf algebroids with algebraic morphisms and then showed that the construction of the biretraction inverse semigroups is functorial. Finally, we are going to discuss some attempts in the opposite direction. This is a joint work with Paolo Saracco.
