Nichols algebras over groups with finite root system of rank two II

Abstract

We classify all non-abelian groups G such that there exists a pair (V,W) of absolutely simple Yetter-Drinfeld modules over G such that the Nichols algebra of the direct sum of V and W is finite-dimensional under two assumptions: the square of the braiding between V and W is not the identity, and G is generated by the support of V and W. As a corollary, we prove that the dimensions of such V and W are at most six. As a tool we use the Weyl groupoid of (V,W).

21 pages. Final version. Accepted for publication in Journal of Group Theory

References in corpus (2)

• Nichols algebras of group type with many quadratic relations
• Nichols algebras over groups with finite root system of rank two III

Cited by in corpus (7)

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• The classification of Nichols algebras over groups with finite root system of rank two
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• An explicit description of the second cohomology group of a quandle
• Nichols algebras over groups with finite root system of rank two III
• PBW deformations of a Fomin-Kirillov algebra and other examples
• Pointed Hopf algebras over non abelian groups with decomposable braidings, I