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

By Pavel Etingof, Shlomo Gelaki. 2002

59 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/4de177bd972b0345acc255a75f25308dd2c03f9b

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Citations in the corpus

Arithmetic Fundamental Groups and Noncommutative Algebra (2002, background): “[EG02], however, drops the semisimple condition based on a strengthening of Deligne's result [DeOl].”
On finite-dimensional Hopf algebras (2014, background): “This lead eventually to the classification 107 of triangular finite-dimensional Hopf algebras [29]; previous work on the semisimple case 108 culminated in [28].”