Positive Hopf Algebras and the Set Theoretical Yang-Baxter Equation

Professor Min Yan
The Hong Kong University of Science and Technology

Friday, January 16, 2004
11:00 am, 845 Patterson Office Tower

Abstract:

A Hopf algebra is positive if it has a basis with respect to which the structure constants are non-negative. We give a complete classification of such Hopf algebras and discuss the positive quasi-triangular structures on such Hopf algebras. The study of the positivity condition in Hopf algebras was motivated by the problem of set-theoretical solutions of the Yang-Baxter equation. We will see how our results can be used to solve the problem.