141 research outputs found
Conjugacy classes of p-cycles of type D in alternating groups
We classify the conjugacy classes of p-cycles of type D in alternating
groups. This finishes the open cases in arXiv:0812.4628. We also determine all
the subracks of those conjugacy classes which are not of type D.Comment: Second paragraph of subsection 2.2 rewritten. 4-th sentence of
subsection 2.4 rewritten. More explanations added in Remark 2.4. Lemma 2.5
and Corollary 2.7 added. Appendix removed and put it as Remark 3.1. Remark
3.2 (former 3.1) reorganized. References: [Da], [EGSS], [H], [IS] added,
[GPPS] removed. Communications in Algebra (2014
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
- …