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

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

2010-11-24

arxiv.org/abs/1011.5267v2

Mathematics

Quantum Algebra

Final version. 9 pages

Scientific paper

10.1090/S0002-9939-2012-11215-8

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.

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