The classification of finite-dimensional triangular Hopf algebras over an algebraically closed field of characteristic 0

Abstract

We explain that a new theorem of Deligne on symmetric tensor categories implies, in a straightforward manner, that any finite dimensional triangular Hopf algebra over an algebraically closed field of characteristic zero has Chevalley property, and in particular the list of finite dimensional triangular Hopf algebras over such a field given in math.QA/0008232, math.QA/0101049 is complete. We also use Deligne's theorem to settle a number of questions about triangular Hopf algebras, raised in our previous publications, and generalize Deligne's result to nondegenerate semisimple categories in characteristic $p$, by using lifting methods developed in math.QA/0203060.

8 pages, latex

References in corpus (3)

• The representation category of the quantum group of a non-degenerate bilinear form
• Schur-Weyl Categories and Non-quasiclassical Weyl Type Formula
• Some Properties of Finite-Dimensional Semisimple Hopf Algebras

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• Non-existence of Hopf orders for a twist of the alternating and symmetric groups
• Existence of integral Hopf orders in twists of group algebras
• Classification of Element Systems over Finite Commutative Groups