247 Citations
Higher Derived Brackets for Arbitrary Derivations
- Mathematics
- 2004
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
- Mathematics
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
- Mathematics
- 2005
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
- Mathematics
- 2004
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
- Mathematics
- 2006
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
- Mathematics
- 2018
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
- Mathematics
- 2009
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
- MathematicsBulletin 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…
A ] 1 1 Ja n 20 07 Higher Derived Brackets and Deformation Theory I
- Mathematics
- 2008
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…
References
SHOWING 1-10 OF 54 REFERENCES
Higher Derived Brackets for Not Necessarily Inner Derivations
- Mathematics
- 2004
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
- Mathematics
- 1997
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
- Mathematics
- 1994
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
- Mathematics
- 2000
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
- Mathematics
- 1999
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.
- Mathematics
- 2001
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
- Mathematics
- 1999
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
- Mathematics
- 1998
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
- Mathematics
- 2002
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…