113 research outputs found
Pointed Hopf Algebras with classical Weyl Groups
We prove that Nichols algebras of irreducible Yetter-Drinfeld modules over
classical Weyl groups supported by are
infinite dimensional, except in three cases. We give necessary and sufficient
conditions for Nichols algebras of Yetter-Drinfeld modules over classical Weyl
groups supported by to be finite dimensional.Comment: Combined with arXiv:0902.4748 plus substantial changes. To appear
International Journal of Mathematic
Braided racks, Hurwitz actions and Nichols algebras with many cubic relations
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.Comment: v2: 35 pages, 6 tables, 14 figure
Braided Bialgebras of Type One
Braided bialgebras of type one in abelian braided monoidal categories are
characterized as braided graded bialgebras which are strongly
-graded both as an algebra and as a coalgebra
Finite dimensional pointed Hopf algebras over S_4
Let k be an algebraically closed field of characteristic 0. We conclude the
classification of finite dimensional pointed Hopf algebras whose group of
group-likes is S_4. We also describe all pointed Hopf algebras over S_5 whose
infinitesimal braiding is associated to the rack of transpositions.Comment: 22 pages. Some results extende
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