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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Author: L. Vendramin
Journal: Proc. Amer. Math. Soc. 140 (2012), 3715-3723
MSC (2010): Primary 16T05, 16T30, 17B37
Published electronically: March 7, 2012
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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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Additional Information

L. Vendramin
Affiliation: Departamento de Matemática – FCEyN, Universidad de Buenos Aires, Pab. I – Ciudad Universitaria (1428), Buenos Aires, Argentina
Email: lvendramin@dm.uba.ar

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11215-8
PII: S 0002-9939(2012)11215-8
Received by editor(s): November 17, 2010
Received by editor(s) in revised form: February 9, 2011, and April 26, 2011
Published electronically: March 7, 2012
Additional Notes: The author’s work was partially supported by CONICET
Communicated by: Gail R. Letzter
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.