Braided racks, Hurwitz actions and Nichols algebras with many cubic relations

2011/03/31 by I. Heckenberger, A. Lochmann, L. Vendramin · 1 citation
Mathematics · #math.QA #msc:16T05 #msc:20F36

paper · pdf · doi:10.1007/s00031-012-9176-7

published as Transform. Groups 17 (2012), no. 1, 157-194 · v2: 35 pages, 6 tables, 14 figures

arxiv created 2011/10/13 · arxiv updated 2012/03/07

Abstract

We classify Nichols algebras of irreducible Yetter-Drinfeld modules over groups such that the underlying rack is braided and the homogeneous component of degree three of the Nichols algebra satisfies a given inequality. This assumption turns out to be equivalent to a factorization assumption on the Hilbert series. Besides the known Nichols algebras we obtain a new example. Our method is based on a combinatorial invariant of the Hurwitz orbits with respect to the action of the braid group on three strands.

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