Deformations of Batalin-Vilkovisky algebras

Kravchenko, Olga

Banach Center Publications, Tome 51 (2000), p. 131-139 / Harvested from The Polish Digital Mathematics Library

Résumé

We show that a graded commutative algebra A with any square zero odd differential operator is a natural generalization of a Batalin-Vilkovisky algebra. While such an operator of order 2 defines a Gerstenhaber (Lie) algebra structure on A, an operator of an order higher than 2 (Koszul-Akman definition) leads to the structure of a strongly homotopy Lie algebra ( $L_{\infty}$ -algebra) on A. This allows us to give a definition of a Batalin-Vilkovisky algebra up to homotopy. We also make a conjecture which is a generalization of the formality theorem of Kontsevich to the Batalin-Vilkovisky algebra level.

Publié le : 2000-01-01

Zbl 1015.17029

EUDML-ID : urn:eudml:doc:209024

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     author = {Kravchenko, Olga},
     title = {Deformations of Batalin-Vilkovisky algebras},
     journal = {Banach Center Publications},
     volume = {51},
     year = {2000},
     pages = {131-139},
     zbl = {1015.17029},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv51z1p131bwm}
}

Kravchenko, Olga. Deformations of Batalin-Vilkovisky algebras. Banach Center Publications, Tome 51 (2000) pp. 131-139. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv51z1p131bwm/

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