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

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

2002-02-25

arxiv.org/abs/math/0202258v3

Mathematics

Quantum Algebra

8 pages, latex

Scientific paper

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.

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