A Hopf Algebra Perspective on Set-Theoretic Pentagon Solutions

Abstract: 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.

Mathematics

Audience: researchers in the topic

European Quantum Algebra Lectures (EQuAL)

Series comments: EQuAL is an online seminar series on quantum algebra and related topics such as topological and conformal field theory, operator algebra, representation theory, quantum topology, etc. sites.google.com/view/equalseminar/home