On the Hopf algebra structure of the Lusztig quantum divided power algebras
[Sur la structure d’algèbre de Hopf des algèbres de puissances divisées quantiques de Lusztig]
Annales Mathématiques Blaise Pascal, Tome 27 (2020) no. 2, pp. 131-157.

Nous étudions la structure d’algèbre de Hopf des groupes quantiques de Lusztig.Tout d’abord, nous montrons que la partie zéro est le produit tensoriel de l’algèbre de groupe d’un groupe abélien fini avec l’algèbre enveloppante d’une algèbre de Lie abélienne. Ensuite, nous les construisons à partir des parties plus, moins et zéro au moyen d’actions et de coactions appropriées par le formalisme de Sommerhäuser pour décrire des décompositions triangulaires.

We study the Hopf algebra structure of Lusztig’s quantum groups. First we show that the zero part is the tensor product of the group algebra of a finite abelian group with the enveloping algebra of an abelian Lie algebra. Second we build them from the plus, minus and zero parts by means of suitable actions and coactions within the formalism presented by Sommerhäuser to describe triangular decompositions.

Publié le :
DOI : https://doi.org/10.5802/ambp.393
Classification : 16T05
Mots clés : Groupes quantiques, algèbres de puissance divisée quantique de Lusztig, algèbres de Nichols
@article{AMBP_2020__27_2_131_0,
     author = {Nicol\'as Andruskiewitsch and Iv\'an Angiono and Cristian Vay},
     title = {On the {Hopf} algebra structure of the {Lusztig}  quantum divided power algebras},
     journal = {Annales Math\'ematiques Blaise Pascal},
     pages = {131--157},
     publisher = {Universit\'e Clermont Auvergne, Laboratoire de math\'ematiques Blaise Pascal},
     volume = {27},
     number = {2},
     year = {2020},
     doi = {10.5802/ambp.393},
     language = {en},
     url = {https://ambp.centre-mersenne.org/articles/10.5802/ambp.393/}
}
Nicolás Andruskiewitsch; Iván Angiono; Cristian Vay. On the Hopf algebra structure of the Lusztig  quantum divided power algebras. Annales Mathématiques Blaise Pascal, Tome 27 (2020) no. 2, pp. 131-157. doi : 10.5802/ambp.393. https://ambp.centre-mersenne.org/articles/10.5802/ambp.393/

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