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Yetter-Drinfel'd Hopf algebras over groups of prime order | | Yorck Sommerhaeuser
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30 May 1999 | | Journal: | Lect. Notes Math., Vol. 1789, Springer, Berlin, 2002 | | Subject: | Rings and Algebras; Quantum Algebra; Representation Theory MSC-class: 16W30 (Primary); 17B37 (Secondary) | math.RA math.QA math.RT | | Abstract: | We prove a structure theorem for Yetter-Drinfel’d Hopf algebras over groups of prime order that are nontrivial, cocommutative, and cosemisimple: Under certain assumptions on the base field, these algebras can be decomposed into a tensor product of the dual group ring of the group of prime order and an ordinary group ring of some other group. This tensor product is a crossed product as an algebra and an ordinary tensor product as a coalgebra. In particular, the dimension of such a Yetter-Drinfel’d Hopf algebra is divisible by the prime under consideration. We also find explicit examples of such Yetter-Drinfel’d Hopf algebras and apply the result to the classification program for semisimple Hopf algebras. | | Source: | arXiv, math.RA/9905191 | | Services: | Forum | Review | PDF | Favorites | |
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