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Title

Deformations of Batalin-Vilkovisky algebras

Authors 1

Affiliations

  1. Institut Girard Desargues (UPRES-A 5028), Université Claude Bernard - Lyon I, 43, boulevard du 11 novembre 1918, 69622 Villeurbanne Cedex, France

Abstract

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∞-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.

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Banach Center Publications
2000/51/1
Export to PBN, Opens in new tab
Pages:
131-139
Main language of publication
English
Published
2000
Exact and natural sciences