PBW deformations of a Fomin-Kirillov algebra and other examples

We begin the study of PBW deformations of graded algebras relevant to the theory of Hopf algebras. One of our examples is the Fomin-Kirillov algebra FK3. Another one appeared in a paper of Garc\'ia Iglesias and Vay. As a consequence of our methods, we determine when the deformations are semisimple and we are able to produce PBW bases and polynomial identities for these deformations.Comment: 22 pages. Accepted for publication in Algebr. Represent. Theor

A classification of Nichols algebras of semi-simple Yetter-Drinfeld modules over non-abelian groups

Over fields of arbitrary characteristic we classify all braid-indecomposable tuples of at least two absolutely simple Yetter-Drinfeld modules over non-abelian groups such that the group is generated by the support of the tuple and the Nichols algebra of the tuple is finite-dimensional. Such tuples are classified in terms of analogs of Dynkin diagrams which encode much information about the Yetter-Drinfeld modules. We also compute the dimensions of these finite-dimensional Nichols algebras. Our proof uses the Weyl groupoid of a tuple of simple Yetter-Drinfeld modules.Comment: 61 pages, 4 tables. Final version. Accepted for publication in J. Europ. Math. So

On Nichols algebras over SL(2,Fq) and GL(2,Fq)

We compute necessary conditions on Yetter-Drinfeld modules over the groups SL(2,Fq) and GL(2,Fq) to generate finite dimensional Nichols algebras. This is a first step towards a classification of pointed Hopf algebras with a group of group-likes isomorphic to one of these groups.Comment: Major exposition revision, including referees remarks. To appear in J. Math. Phys. 13 page

Electric dipole and magnetic quadrupole moments of the WW boson via a CP-violating HWWHWW vertex in effective Lagrangians

The possibility of nonnegligible $W$ electric dipole ($\widetilde{\mu}_W$) and magnetic quadrupole ($\widetilde{Q}_W$) moments induced by the most general $HWW$ vertex is examined via the effective Lagrangian technique. It is assumed that new heavy fermions induce an anomalous CP-odd component of the $HWW$ vertex, which can be parametrized by an $SU_L(2)\times U_Y(1)$-invariant dimension-six operator. This anomalous contribution, when combined with the standard model CP-even contribution, lead to CP-odd electromagnetic properties of the $W$ boson, which are characterized by the form factors $\Delta \widetilde{\kappa}$ and $\Delta \widetilde{Q}$. It is found that $\Delta \widetilde{\kappa}$ is divergent, whereas $\Delta \widetilde{Q}$ is finite, which reflects the fact that the latter cannot be generated at the one-loop level in any renormalizable theory. Assuming reasonable values for the unknown parameters, we found that $\widetilde{\mu}_W\sim 3-6\times 10^{-21}$ e-cm, which is eight orders of magnitude larger than the SM prediction and close to the upper bound derived from the neutron electric dipole moment. The estimated size of the somewhat less-studied $\widetilde{Q}_W$ moment is of the order of $-10^{-36}$ e-cm^2, which is fifteen orders of magnitude above the SM contribution.Comment: 7 pages, 6 figures, REVTEX styl

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