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

Vendramin, L.

doi:10.1090/S0002-9939-2012-11215-8

Nichols algebras associated to the transpositions of the symmetric group are twist-equivalent
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by L. Vendramin PDF

Proc. Amer. Math. Soc. 140 (2012), 3715-3723 Request permission

Abstract:

Using the theory of covering groups of Schur we prove that the two Nichols algebras associated to the conjugacy class of transpositions in $\mathbb {S}_n$ 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 the quantum cohomology ring of flag manifolds.

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