Matthew Alexander - Algebra Seminar

Abstract:

Hopf algebras and Frobenius algebras are two structures that have found important roles in formulating quantum field theory: Hopf algebras in the guise of quantum groups, and Frobenius algebras in the realm of topological quantum field theories. In this talk we will introduce these two algebras and motivate their use in defining a compatibility structure between them, called a Hopf-Frobenius module, which can be used to generalize the geometric, analytic, and algebraic structures that appear in quantum field theory.