Comptes Rendus
no. 4
Lie algebras/Mathematical physics
Generalized cluster structure on the Drinfeld double of GLn

Presented by: the Editorial Board

Michael Gekhtman1; Michael Shapiro2; Alek Vainshtein3
1 Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556, USA
2 Department of Mathematics, Michigan State University, East Lansing, MI 48823, USA
3 Department of Mathematics & Department of Computer Science, University of Haifa, Haifa, Mount Carmel 31905, Israel
Comptes Rendus. Mathématique, Volume 354 (2016) no. 4, pp. 345-349.

We construct a generalized cluster structure compatible with the Poisson bracket on the Drinfeld double of the standard Poisson–Lie group GLn and derive from it a generalized cluster structure in GLn compatible with the push-forward of the dual Poisson–Lie bracket.

On construit des structures d'algèbres amassées généralisées compatibles avec le crochet de Poisson sur le double de Drinfeld du group GLn muni de sa structure de Poisson–Lie usuelle. On en déduit une structure d'algèbre amassée généralisée sur GLn compatible avec l'image directe du crochet de Poisson dual.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2016.01.006

Michael Gekhtman 1; Michael Shapiro 2; Alek Vainshtein 3

1 Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556, USA
2 Department of Mathematics, Michigan State University, East Lansing, MI 48823, USA
3 Department of Mathematics & Department of Computer Science, University of Haifa, Haifa, Mount Carmel 31905, Israel 
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Michael Gekhtman; Michael Shapiro; Alek Vainshtein. Generalized cluster structure on the Drinfeld double of GLn. Comptes Rendus. Mathématique, Volume 354 (2016) no. 4, pp. 345-349. doi : 10.1016/j.crma.2016.01.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.01.006/

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