[Structures d'algébres amassées généralisées sur le double de Drinfeld du group GLn]
On construit des structures d'algèbres amassées généralisées compatibles avec le crochet de Poisson sur le double de Drinfeld du group muni de sa structure de Poisson–Lie usuelle. On en déduit une structure d'algèbre amassée généralisée sur compatible avec l'image directe du crochet de Poisson dual.
We construct a generalized cluster structure compatible with the Poisson bracket on the Drinfeld double of the standard Poisson–Lie group and derive from it a generalized cluster structure in compatible with the push-forward of the dual Poisson–Lie bracket.
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@article{CRMATH_2016__354_4_345_0,
author = {Gekhtman, Michael and Shapiro, Michael and Vainshtein, Alek},
title = {Generalized cluster structure on the {Drinfeld} double of {\protect\emph{GL}\protect\textsubscript{\protect\emph{n}}}},
journal = {Comptes Rendus. Math\'ematique},
pages = {345--349},
publisher = {Elsevier},
volume = {354},
number = {4},
year = {2016},
doi = {10.1016/j.crma.2016.01.006},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2016.01.006/}
}
TY - JOUR AU - Gekhtman, Michael AU - Shapiro, Michael AU - Vainshtein, Alek TI - Generalized cluster structure on the Drinfeld double of GLn JO - Comptes Rendus. Mathématique PY - 2016 SP - 345 EP - 349 VL - 354 IS - 4 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2016.01.006/ DO - 10.1016/j.crma.2016.01.006 LA - en ID - CRMATH_2016__354_4_345_0 ER -
%0 Journal Article %A Gekhtman, Michael %A Shapiro, Michael %A Vainshtein, Alek %T Generalized cluster structure on the Drinfeld double of GLn %J Comptes Rendus. Mathématique %D 2016 %P 345-349 %V 354 %N 4 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2016.01.006/ %R 10.1016/j.crma.2016.01.006 %G en %F CRMATH_2016__354_4_345_0
Gekhtman, Michael; Shapiro, Michael; Vainshtein, Alek. Generalized cluster structure on the Drinfeld double of GLn. Comptes Rendus. Mathématique, Tome 354 (2016) no. 4, pp. 345-349. doi : 10.1016/j.crma.2016.01.006. http://www.numdam.org/articles/10.1016/j.crma.2016.01.006/
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