## Quantum Topology / Hopf Algebra Seminar

David Simpson

UIC

From the Bracket Polynomial to Hopf Algebras

**Abstract:**A matrix model for the bracket polynomial and a solution of the Yang-Baxter equation can be constructed by using a deformed epsilon matrix {e}. The group SL(2) can be defined to be the set of 2x2 matrices such that PeP^T = e where e is the usual epsilon matrix. By generalizing to matrices such that P{e}P^T = {e} and P^T {e}P = {e} we find that the entries of P are elements of a non-commutative algebra, with specific relations. These generate the Hopf algebra (aka quantum group) SL(2)_q. This talk and its sequel will discuss this construction.

Tuesday October 17, 2017 at 3:00 PM in SEO 612