Nichols algebras associated to the transpositions of the symmetric group are twist-equivalent
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- by L. Vendramin
- Proc. Amer. Math. Soc. 140 (2012), 3715-3723
- DOI: https://doi.org/10.1090/S0002-9939-2012-11215-8
- 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.References
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Bibliographic Information
- L. Vendramin
- Affiliation: Departamento de Matemática – FCEyN, Universidad de Buenos Aires, Pab. I – Ciudad Universitaria (1428), Buenos Aires, Argentina
- MR Author ID: 829575
- Email: lvendramin@dm.uba.ar
- 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
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 140 (2012), 3715-3723
- MSC (2010): Primary 16T05, 16T30, 17B37
- DOI: https://doi.org/10.1090/S0002-9939-2012-11215-8
- MathSciNet review: 2944712