کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4587667 | 1630561 | 2008 | 17 صفحه PDF | دانلود رایگان |
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 , where Λ is an integral of H and is the left adjoint action of H on itself. We describe 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 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 .
Journal: Journal of Algebra - Volume 320, Issue 12, 15 December 2008, Pages 4300-4316