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

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

2011-03-23

arxiv.org/abs/1103.4526v2

Transform. Groups 17 (2012), no. 1, 157-194

Mathematics

Quantum Algebra

v2: 35 pages, 6 tables, 14 figures

Scientific paper

10.1007/s00031-012-9176-7

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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