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
43
Background Citations
104
Methods Citations
65
Results Citations
7

247 Citations

Higher Derived Brackets for Arbitrary 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…
Higher Derived Brackets for Arbitrary Derivations by Theodore
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…
Equivalences of higher derived brackets
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
  • Mathematics
    Bulletin of the Malaysian Mathematical Sciences Society
  • 2021
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…
Derived brackets and sh Leibniz algebras
...
...

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…
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…
On some generalizations of Batalin-Vilkovisky algebras
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…
On the structure of graded symplectic supermanifolds and Courant algebroids
This paper is devoted to a study of geometric structures expressible in terms of graded symplectic supermanifolds. We extend the classical BRST formalism to arbitrary pseudo-Euclidean vector bundles…
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…
...
...