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Clifford Correspondence for Finite Dimensional Hopf Algebras

✍ Scribed by S.J Witherspoon

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
100 KB
Volume
218
Category
Article
ISSN
0021-8693

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✦ Synopsis

Let Bΰ » H be a crossed product algebra over an algebraically closed field, with H a finite dimensional Hopf algebra. We give an explicit equivalence between the category of finite dimensional Bΰ » H-modules whose restriction to B is a direct sum of copies of a stable irreducible B-module, and the category of modules for a twisted product of H with the field. This describes all finite dimensional irreducible Bΰ » H-modules containing a stable irreducible B-submodule, and thus generalizes the classical stable Clifford correspondence for groups. In case H is cocommutative, we extend this correspondence to the nonstable case.

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