Polynomial invariants for a semisimple and cosemisimple Hopf algebra of finite dimension Dedicated to Professor Noriaki Kawanaka on the occasion of his 60th birthday

We introduce new polynomial invariants of a finite-dimensional semisimple and cosemisimple Hopf algebra A over a field k by using the braiding structures of A. We investigate basic properties of the polynomial invariants including stability under extension of the base field. Furthermore, we show that our polynomial invariants are indeed tensor invariants of the representation category of A, and recognize the difference of the representation category and the representation ring of A. Actually, by computing and comparing polynomial invariants, we find new examples of pairs of Hopf algebras whose representation rings are isomorphic, but representation categories are distinct. Mathematics Subject Classifications (2000): 16W30, 18D10, 19A49