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
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References

SHOWING 1-10 OF 54 REFERENCES
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
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
We show that a graded commutative algebra A with any square zero odd dif- ferential operator is a natural generalization of a Batalin-Vilkovisky algebra. While such an operator of order 2 defines a
A homotopy Lie-Rinehart resolution and classical BRST cohomology.
We use an interlaced inductive procedure reminiscent of the integration process from traditional deformation theory to construct a homotopy Lie-Rinehart resolution for the Lie-Rinehart pair which
Courant algebroids, derived brackets and even symplectic supermanifolds
In this dissertation we study Courant algebroids, objects that first appeared in the work of T. Courant on Dirac structures; they were later studied by Liu, Weinstein and Xu who used Courant
Courant Algebroids and Strongly Homotopy Lie Algebras
Courant algebroids are structures which include as examples the doubles of Lie bialgebras and the direct sum of tangent and cotangent bundles with the bracket introduced by T. Courant for the study
On odd Laplace operators. II
We analyze geometry of the second order differential operators, having in mind applications to Batalin--Vilkovisky formalism in quantum field theory. As we show, an exhaustive picture can be obtained
...
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