Pointed Hopf algebras over some sporadic simple groups

N. Andruskiewitsch; F. Fantino; M. Graña; L. Vendramin

doi:10.1016/j.crma.2010.04.023

Algebra/Group Theory

Pointed Hopf algebras over some sporadic simple groups
[Algèbres de Hopf pointées sur quelques groupes simples sporadiques]

Présenté par : Jean-Pierre Serre

N. Andruskiewitsch ¹ ; F. Fantino ¹ ; M. Graña ² ; L. Vendramin ^2,³

¹ Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba. CIEM – CONICET. Medina Allende s/n (5000) Ciudad Universitaria, Córdoba, Argentina
² Departamento de Matemática – FCEyN, Universidad de Buenos Aires, Pab. I – Ciudad Universitaria (1428) Buenos Aires, Argentina
³ Instituto de Ciencias, Universidad de Gral. Sarmiento, J.M. Gutierrez 1150, Los Polvorines (1653), Buenos Aires, Argentina

Comptes Rendus. Mathématique, Volume 348 (2010) no. 11-12, pp. 605-608.

Résumé
Abstract

Soit G un groupe sporadique différent du groupe de Fischer ${Fi}_{22}$ , du bébé monstre B et du monstre M. Soit H une algèbre de Hopf complexe pointée de dimension finie dont le groupe des éléments dont le co-produit est égal au carré tensoriel est isomorphisme à G, alors H est isomorphe a l'algèbre de groupe de G.

Any finite-dimensional complex pointed Hopf algebra with group of group-likes isomorphic to a sporadic group, with the possible exception of the Fischer group ${Fi}_{22}$ , the Baby Monster B and the Monster M, is a group algebra.

Reçu le : 2009-02-11
Accepté le : 2010-04-06
Publié le : 2010-05-10

DOI : 10.1016/j.crma.2010.04.023

Affiliations des auteurs :

N. Andruskiewitsch ¹ ; F. Fantino ¹ ; M. Graña ² ; L. Vendramin ^{2, 3}

¹ Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba. CIEM – CONICET. Medina Allende s/n (5000) Ciudad Universitaria, Córdoba, Argentina
² Departamento de Matemática – FCEyN, Universidad de Buenos Aires, Pab. I – Ciudad Universitaria (1428) Buenos Aires, Argentina
³ Instituto de Ciencias, Universidad de Gral. Sarmiento, J.M. Gutierrez 1150, Los Polvorines (1653), Buenos Aires, Argentina

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     author = {N. Andruskiewitsch and F. Fantino and M. Gra\~na and L. Vendramin},
     title = {Pointed {Hopf} algebras over some sporadic simple groups},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {605--608},
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     volume = {348},
     number = {11-12},
     year = {2010},
     doi = {10.1016/j.crma.2010.04.023},
     language = {en},
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N. Andruskiewitsch; F. Fantino; M. Graña; L. Vendramin. Pointed Hopf algebras over some sporadic simple groups. Comptes Rendus. Mathématique, Volume 348 (2010) no. 11-12, pp. 605-608. doi : 10.1016/j.crma.2010.04.023. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.04.023/

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Cité par Sources :

^☆ Some of the results presented here are part of the PhD theses of F.F. and L.V., work under the supervision of N.A. and M.G., respectively. This work was partially supported by ANPCyT-Foncyt, CONICET, Ministerio de Ciencia y Tecnología (Córdoba) and Secyt (UNC).

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