A method of construction of finite-dimensional triangular semisimple Hopf algebras

1998/06/12 by Pavel Etingof, Shlomo Gelaki, Etingof, Pavel +1 · 1 citation
Mathematics · #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA

paper · pdf · doi:10.48550/arxiv.math/9806072

9 pages, amstex

arxiv created 1998/06/12 · arxiv updated 2009/11/30

Abstract

The goal of this paper is to give a new method of constructing finite-dimensional semisimple triangular Hopf algebras, including minimal ones which are non-trivial (i.e. not group algebras). The paper shows that such Hopf algebras are quite abundant. It also discovers an unexpected connection of such Hopf algebras with bijective 1-cocycles on finite groups and set-theoretical solutions of the quantum Yang-Baxter equation defined by Drinfeld.

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