A Hopf Algebra Perspective on Set-Theoretic Pentagon Solutions (Ilaria Colazzo, University of Leeds)

05.03.2026 14:15

In this talk I will report on joint work with Janssens. We investigate the connection between bijective set-theoretic solutions of the pentagon equation and Hopf algebras. In the finite setting, we show that such solutions correspond to Hopf algebras with the positive basis property, and as a corollary we generalise the Lu–Yan–Zhu classification to arbitrary characteristic 0 fields. We also address the more general question of when a Hopf algebra admits a basis that yields a set-theoretic solution. If time permits, we will discuss classification results in the (co)commutative case. I will explain the main ideas of the constructions and illustrate the results with examples.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-15, Séminaire "Topologie et géométrie"

entrée libre