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- W2007250079 abstract "We study certain aspects of finite-dimensional non-semisimple symmetric Hopf algebras H and their duals H ∗ . We focus on the set I ( H ) of characters of projective H -modules which is an ideal of the algebra of cocommutative elements of H ∗ . This ideal corresponds via a symmetrizing form to the projective center (Higman ideal) of H which turns out to be Λ H , where Λ is an integral of H and is the left adjoint action of H on itself. We describe Λ H via primitive and central primitive idempotents of H . We also show that it is stable under the quantum Fourier transform. Our best results are obtained when H is a factorizable ribbon Hopf algebra over an algebraically closed field of characteristic 0. In this case Λ H is also the image of I ( H ) under a “translated” Drinfel'd map. We use this fact to prove the existence of a Steinberg-like character. The above ingredients are used to prove a Verlinde-type formula for Λ H ." @default.
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- W2007250079 date "2008-12-01" @default.
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- W2007250079 title "Characters and a Verlinde-type formula for symmetric Hopf algebras" @default.
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- W2007250079 doi "https://doi.org/10.1016/j.jalgebra.2008.08.025" @default.
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