The Representation Theory of Co-triangular Semisimple Hopf Algebras

Details The Representation Theory of Co-triangular Semisimple Hopf Algebras The Representation Theory of Co-triangular Semisimple Hopf Algebras

1998-12-18

arxiv.org/abs/math/9812118v1

Mathematics

Quantum Algebra

7 pages, latex

Scientific paper

In a previous paper we prove that any semisimple triangular Hopf algebra A over an algebraically closed field of characteristic 0 (say the field of complex numbers C) is obtained from a finite group after twisting the ordinary comultiplication of its group algebra in the sense of Drinfeld; that is A=C[G]^J for some finite group G and a twist J\in C[G]\ot C[G]. In this paper we explicitly describe the representation theory of co-triangular semisimple Hopf algebras A^*=(C[G]^J)^* in terms of representations of some associated groups. As a corollary we prove that Kaplansky's 6th conjecture from 1975 holds for A^*; that is that the dimension of any irreducible representation of A^* divides the dimension of A.

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