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Yvette Kosmann-Schwarzbach
From Poisson algebras to Gerstenhaber algebras
Annales de l'institut Fourier, 46 no. 5 (1996), p. 1243-1274, doi: 10.5802/aif.1547
Article PDF | Analyses MR 98b:17032 | Zbl 0858.17027 | 3 citations dans Cedram

Résumé - Abstract

On montre que l’on peut construire un crochet de Poisson pair à partir d’un crochet de Gerstenhaber, à l’aide d’une dérivation impaire de carré nul, dans la catégorie des algèbres de Loday (algèbres munies d’un crochet non antisymétrique, généralisant les crochets de Lie, appelées jusqu’à présent dans la littérature, algèbres de Leibniz). Ces ``crochets dérivés" donnent des crochets de Lie sur certains quotients, et sur certaines sous-algèbres abéliennes. On peut expliquer ainsi l’origine du crochet de Lie sur l’espace des formes différentielles co-exactes sur une variété de Poisson. Nous étudions les crochets dérivés sur l’espace des cochaînes sur une algèbre associative ou de Lie. Enfin nous relions les résultats précédents à diverses généralisations de la notion d’algèbre de Batalin-Vilkovisky.

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