## 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…

## References

SHOWING 1-10 OF 54 REFERENCES

Higher Derived Brackets for Not Necessarily Inner Derivations

- Mathematics
- 2004

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…

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…

On the structure of graded symplectic supermanifolds and Courant algebroids

- Mathematics
- 2002

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

- 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…