Navegar

Colección

Datos Estadísticas

Artículo

Estamos trabajando para incorporar este artículo al repositorio
Consulte el artículo en la página del editor
Consulte la política de Acceso Abierto del editor

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 the quantum cohomology ring of flag manifolds. © 2012 American Mathematical Society.

Registro:

Documento: Artículo
Título:Nichols algebras associated to the transpositions of the symmetric group are twist-equivalent
Autor:Vendramin, L.
Filiación:Departamento de Matemática - FCEyN, Universidad de Buenos Aires, Pab. I - Ciudad Universitaria (1428), Buenos Aires, Argentina
Año:2012
Volumen:140
Número:11
Página de inicio:3715
Página de fin:3723
DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11215-8
Título revista:Proceedings of the American Mathematical Society
Título revista abreviado:Proc. Am. Math. Soc.
ISSN:00029939
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v140_n11_p3715_Vendramin

Referencias:

  • Andruskiewitsch, N., Fantino, F., García, G.A., Vendramin, L., On Nichols algebras associated to simple racks (2011) Contemp. Math, 537, pp. 31-56. , Amer. Math. Soc., Providence, RI
  • Andruskiewitsch, N., Fantino, F., Graña, M., Vendramin, L., Finite-dimensional pointed Hopf algebras with alternating groups are trivial (2011) Ann. Mat. Pura Appl, 190 (2-4), pp. 225-245. , MR2786171
  • Andruskiewitsch, N., Graña, M., From racks to pointed Hopf algebras (2003) Adv. Math, 178 (2), pp. 177-243. , MR1994219 (2004i:16046)
  • Andruskiewitsch, N., Schneider, H.-J., Pointed Hopf algebras (2002) New Directions In Hopf Algebras, Math. Sci. Res. Inst. Publ, 43, pp. 1-68. , Cambridge Univ. Press, Cambridge, MR1913436 (2003e:16043)
  • Andruskiewitsch, N., Schneider, H.-J., On the classification of finite-dimensional pointed Hopf algebras (2010) Ann. of Math, 171 (1-2), pp. 375-417. , MR2630042 (2011j:16058)
  • Bazlov, Y., Nichols-Woronowicz algebra model for Schubert calculus on Coxeter groups (2006) J. Algebra, 297 (2), pp. 372-399. , MR2209265 (2007b:20083)
  • Berkovich, Y.G., Zhmud', E.M., Characters of finite groups. Part 1 (1998) Translations of Mathematical Monographs, 172. , American Mathematical Society, Providence, RI, MR1486039 (98m:20011)
  • Borel, A., Sur la cohomologie des espaces fibrés principaux et des espaces homogènes de groupes de Lie compacts (1953) Ann. of Math, 57 (2), pp. 115-207. , (French). MR0051508 (14:490e)
  • Carter, J.S., Jelsovsky, D., Kamada, S., Langford, L., Saito, M., Quandle cohomology and state-sum invariants of knotted curves and surfaces (2003) Trans. Amer. Math. Soc, 355 (10), pp. 3947-3989. , MR1990571 (2005b:57048)
  • Doi, Y., Takeuchi, M., Multiplication alteration by two-cocycles-the quantum version (1994) Comm. Algebra, 22 (14), pp. 5715-5732. , MR1298746 (95j:16043)
  • Fomin, S., Kirillov, A.N., Quadratic algebras, Dunkl elements, and Schubert calculus (1999) Advances In Geometry, Progr. Math, 172, pp. 147-182. , Birkhäuser Boston, Boston, MA, MR1667680 (2001a:05152)
  • García, G.A., García, I.A., Finite dimensional pointed Hopf algebras over S 4 (2011) Israel J. Math, 183, pp. 417-444. , MR2811166
  • Graña, M., On Nichols algebras of low dimension (2000) New Trends In Hopf Algebra Theory (La Falda, 1999), Contemp. Math, 267, pp. 111-134. , Amer. Math. Soc., Providence, RI
  • Graña, M., Nichols Algebras of Non-abelian Group Type: Zoo of Examples, , http://mate.dm.uba.ar/matiasg/zoo, Web page available at
  • Graña, M., Heckenberger, I., Vendramin, L., Nichols algebras of group type with many quadratic relations (2011) Adv. Math, 227 (5), pp. 1956-1989. , MR2803792
  • Heckenberger, I., The Weyl groupoid of a Nichols algebra of diagonal type (2006) Invent. Math, 164 (1), pp. 175-188. , MR2207786 (2007e:16047)
  • Heckenberger, I., Classification of arithmetic root systems (2009) Adv. Math, 220 (1), pp. 59-124. , MR2462836 (2009k:17017)
  • Karpilovsky, G., The Schur multiplier (1987) London Mathematical Society Monographs. New Series, 2. , The Clarendon Press, Oxford University Press, New York, MR1200015 (93j:20002)
  • Majid, S., Noncommutative differentials and Yang-Mills on permutation groups S n (2005) Hopf Algebras In Noncommutative Geometry and Physics, Lecture Notes In Pure and Appl. Math, 239, pp. 189-213. , Dekker, New York, MR2106930 (2006b:58007)
  • Majid, S., Oeckl, R., Twisting of quantum differentials and the Planck scale Hopf algebra (1999) Comm. Math. Phys, 205 (3), pp. 617-655. , MR1711340 (2000h:58018)
  • Milinski, A., Schneider, H.-J., Pointed indecomposable Hopf algebras over Coxeter groups (2000) New Trends In Hopf Algebra Theory (La Falda, 1999), Contemp. Math, 267, pp. 215-236. , Amer. Math. Soc., Providence, RI, MR1800714 (2001k:16074)
  • Schur, J., On the representation of the symmetric and alternating groups by fractional linear substitutions (2001) Internat. J. Theoret. Phys, 40 (1), pp. 413-458. , Translated from the German [J. Reine Angew. Math. 139 (1911), 155-250] by Marc-Felix Otto. MR1820589 (2003a:20016)
  • Wilson, R.A., The finite simple groups (2009) Graduate Texts In Mathematics, 251. , Springer-Verlag, London Ltd., London, MR2562037 (2011e:20018)

Citas:

---------- APA ----------
(2012) . Nichols algebras associated to the transpositions of the symmetric group are twist-equivalent. Proceedings of the American Mathematical Society, 140(11), 3715-3723.
http://dx.doi.org/10.1090/S0002-9939-2012-11215-8
---------- CHICAGO ----------
Vendramin, L. "Nichols algebras associated to the transpositions of the symmetric group are twist-equivalent" . Proceedings of the American Mathematical Society 140, no. 11 (2012) : 3715-3723.
http://dx.doi.org/10.1090/S0002-9939-2012-11215-8
---------- MLA ----------
Vendramin, L. "Nichols algebras associated to the transpositions of the symmetric group are twist-equivalent" . Proceedings of the American Mathematical Society, vol. 140, no. 11, 2012, pp. 3715-3723.
http://dx.doi.org/10.1090/S0002-9939-2012-11215-8
---------- VANCOUVER ----------
Vendramin, L. Nichols algebras associated to the transpositions of the symmetric group are twist-equivalent. Proc. Am. Math. Soc. 2012;140(11):3715-3723.
http://dx.doi.org/10.1090/S0002-9939-2012-11215-8