Conjugacy Classes,Class Sums and Character Tables for Hopf Algebras |
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Authors: | Miriam Cohen |
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Institution: | Department of Mathematics , Ben Gurion University , Beer Sheva, Israel |
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Abstract: | We extend the notion of conjugacy classes and class sums from finite groups to semisimple Hopf algebras and show that the conjugacy classes are obtained from the factorization of H as irreducible left D(H)-modules. For quasitriangular semisimple Hopf algebras H, we prove that the product of two class sums is an integral combination of the class sums up to d ?2 where d = dim H. We show also that in this case the character table is obtained from the S-matrix associated to D(H). Finally, we calculate explicitly the generalized character table of D(kS 3), which is not a character table for any group. It moreover provides an example of a product of two class sums which is not an integral combination of class sums. |
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Keywords: | Character algebras Character table Class sums Conjugacy classes S-matrix Semisimple Hopf algebras |
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