POLYNOMIAL INVARIANTS OF FINITE-DIMENSIONAL HOPF ALGEBRAS DERIVED FROM BRAIDING STRUCTURES

Abstract. We introduce invariants of a finite-dimensional semisimple and cosemisimple Hopf algebra A over a field k by using the braiding structures of A. The invariants are given in the form of polynomials. The polynomials have integral coefficients under some condition, and become stable by taking some suitable extension of the base field. Furthermore, the polynomials give invariants of the representation category of a finite-dimensional semisimple and cosemisimple Hopf algebra under k-linear tensor equivalence. By using the polynomials, we can find some pairs of Hopf algebras, whose representation rings are same, but representation categories are different. 1