Nichols algebras associated to the transpositions of the symmetric group are twist-equivalent

2010/11/30 by L. Vendramin · 1 citation
Mathematics · #math.QA #msc:16T05 #msc:16T30 #msc:17B37

paper · pdf · doi:10.1090/s0002-9939-2012-11215-8

published as Proc. Amer. Math. Soc. 140 (2012), 3715-3723 · Final version. 9 pages

arxiv created 2011/04/27 · arxiv updated 2012/09/11

Abstract

Using the theory of covering groups of Schur we prove that the two Nichols algebras associated to the conjugacy class of transpositions in S_n are equivalent by twist and hence they have the same Hilbert series. These algebras appear in the classification of pointed Hopf algebras and in the study of quantum cohomology ring of flag manifolds.

Cited by

• Point modules of Nichols algebras over non-abelian groups