Higher derived brackets and homotopy algebras

@article{Voronov2005HigherDB,
  title={Higher derived brackets and homotopy algebras},
  author={Theodore Th. Voronov},
  journal={Journal of Pure and Applied Algebra},
  year={2005},
  volume={202},
  pages={133-153}
}
  • T. Voronov
  • Published 3 April 2003
  • Mathematics
  • Journal of Pure and Applied Algebra
View PDF on arXiv
247 Citations
Highly Influential Citations
44
Background Citations
105
Methods Citations
65
Results Citations
7

247 Citations

Higher Derived Brackets for Arbitrary Derivations
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We introduce and study a construction of higher derived brackets generated by a (not necessarily inner) derivation of a Lie superalgebra. Higher derived brackets generated by an element of a Lie…
Higher Derived Brackets and Deformation Theory I
The existing constructions of derived Lie and sh-Lie brackets involve multilinear maps that are used to define higher order differential operators. In this paper, we prove the equivalence of three…
Higher Derived Brackets for Not Necessarily Inner Derivations
We introduce and study a construction of higher derived brackets generated by a (not necessarily inner) derivation of a Lie superalgebra. Higher derived brackets generated by an element of a Lie…
Non-Commutative Batalin-Vilkovisky Algebras, Homotopy Lie Algebras and the Courant Bracket
We consider two different constructions of higher brackets. First, based on a Grassmann-odd, nilpotent Δ operator, we define a non-commutative generalization of the higher Koszul brackets, which are…
Homotopy Loday Algebras and Symplectic $2$-Manifolds
Using the technique of higher derived brackets developed by Voronov, we construct a homotopy Loday algebra in the sense of Ammar and Poncin associated to any symplectic $2$-manifold. The algebra we…
Higher derived brackets, strong homotopy associative algebras and Loday pairs
We give a quick method of constructing strong homotopy associative algebra, namely, the higher derived product construction. This method is associative analogue of classical higher derived bracket…
Extensions and Deformations of Algebras with Higher Derivations
  • A. Das
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    Bulletin of the Malaysian Mathematical Sciences Society
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Higher derivations on an associative algebra generalize higher-order derivatives. We call a tuple consisting of an algebra and a higher derivation on it by an AssHDer pair. We define cohomology for…
Kirillov structures up to homotopy
A ] 1 1 Ja n 20 07 Higher Derived Brackets and Deformation Theory I
The existing constructions of derived Lie and sh-Lie brackets involve multilinear maps that are used to define higher order differential operators. In this paper, we prove the equivalence of three…
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References

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Higher Derived Brackets for Not Necessarily Inner Derivations
We introduce and study a construction of higher derived brackets generated by a (not necessarily inner) derivation of a Lie superalgebra. Higher derived brackets generated by an element of a Lie…
A Master Identity for Homotopy Gerstenhaber Algebras
Abstract:We produce a master identity for a certain type of homotopy Gerstenhaber algebras, in particular suitable for the prototype, namely the Hochschild complex of an associative algebra. This…
The Lie algebra structure of tangent cohomology and deformation theory
Strongly homotopy Lie algebras
The present paper can be thought of as a continuation of the paper "Introduction to sh Lie algebras for physicists" by T. Lada and J. Stasheff (International Journal of Theoretical Physics Vol. 32,…
Homotopy Gerstenhaber algebras
The purpose of this paper is to complete Getzler-Jones’ proof of Deligne’s Conjecture, thereby establishing an explicit relationship between the geometry of configurations of points in the plane and…
Deformations of Batalin-Vilkovisky algebras
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Courant Algebroids and Strongly Homotopy Lie Algebras
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On odd Laplace operators. II
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