JournalsjemsVol. 19, No. 7pp. 1977–2017

The classification of Nichols algebras over groups with finite root system of rank two

  • István Heckenberger

    Universität Marburg, Germany
  • Leandro Vendramin

    Universidad de Buenos Aires, Argentina
The classification of Nichols algebras over groups with finite root system of rank two cover
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Abstract

We classify all groups GG and all pairs (V,W)(V,W) of absolutely simple Yetter–Drinfeld modules over GG such that the support of VWV\oplus W generates GG, cW,VcV,Widc_{W,V}c_{V,W}\ne\mathrm {id}, and the Nichols algebra of the direct sum of VV and WW admits a finite root system. As a byproduct, we determine the dimensions of such Nichols algebras, and several new families of finite-dimensional Nichols algebras are obtained. Our main tool is the Weyl groupoid of pairs of absolutely simple Yetter–Drinfeld modules over groups.

Cite this article

István Heckenberger, Leandro Vendramin, The classification of Nichols algebras over groups with finite root system of rank two. J. Eur. Math. Soc. 19 (2017), no. 7, pp. 1977–2017

DOI 10.4171/JEMS/711