Braided racks, Hurwitz actions and Nichols algebras with many cubic relations |
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Authors: | I Heckenberger A Lochmann L Vendramin |
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Institution: | 1. Philipps-Universit?t Marburg, FB Mathematik und Informatik, Hans-Meerwein-Stra?e, 35032, Marburg, Germany 2. Depto. de Matem??tica, FCEyN, Universidad de Buenos Aires, Pab. 1, Ciudad Universitaria (1428), Buenos Aires, Argentina
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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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Keywords: | |
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