Deformations of Batalin-Vilkovisky algebras

Olga Kravchenko

Banach Center Publications (2000)

  • Volume: 51, Issue: 1, page 131-139
  • ISSN: 0137-6934

Abstract

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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.

How to cite

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Kravchenko, Olga. "Deformations of Batalin-Vilkovisky algebras." Banach Center Publications 51.1 (2000): 131-139. <http://eudml.org/doc/209024>.

@article{Kravchenko2000,
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.},
author = {Kravchenko, Olga},
journal = {Banach Center Publications},
keywords = {second order differential operator of square zero; graded commutative algebra; Batalin-Vilkovisky algebra; strongly homotopy Lie algebra; formality theorem of Kontsevich},
language = {eng},
number = {1},
pages = {131-139},
title = {Deformations of Batalin-Vilkovisky algebras},
url = {http://eudml.org/doc/209024},
volume = {51},
year = {2000},
}

TY - JOUR
AU - Kravchenko, Olga
TI - Deformations of Batalin-Vilkovisky algebras
JO - Banach Center Publications
PY - 2000
VL - 51
IS - 1
SP - 131
EP - 139
AB - 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.
LA - eng
KW - second order differential operator of square zero; graded commutative algebra; Batalin-Vilkovisky algebra; strongly homotopy Lie algebra; formality theorem of Kontsevich
UR - http://eudml.org/doc/209024
ER -

References

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