Related papers: Lie Atoms and their deformation theory
This work explores the deformation theory of algebraic structures in a very general setting. These structures include commutative, associative algebras, Lie algebras, and the infinity versions of these structures, the strongly homotopy…
We introduce a new cohomology theory related to deformations of Lie algebra morphisms. This notion involves simultaneous deformations of two Lie algebras and a homomorphism between them.
The aim of this paper is to review the deformation theory of $n$-Lie algebras. We summarize the 1-parameter formal deformation theory and provide a generalized approach using any unital commutative associative algebra as a deformation base.…
A description of a ring of functions on the base of a universal formal deformation for several moduli problems is given. The answer is given in terms of a homology group of a certain dg Lie algebra canonically (up to an essentially unique…
The study of $n$-Lie algebras which are natural generalization of Lie algebras is motivated by Nambu Mechanics and recent developments in String Theory and M-branes. The purpose of this paper is to define cohomology complexes and study…
We compare the second adjoint and trivial Leibniz cohomology spaces of a Lie algebra to the usual ones by a very elementary approach. The comparison gives some conditions, which are easy to verify for a given Lie algebra, for deciding…
The purpose of this paper is to study deformation theory of Hom-associative algebra morphisms and Hom-Lie algebra morphisms. We introduce a suitable cohomology and discuss Infinitesimal deformations, equivalent deformations and…
Cohomology and deformation theories are developed for Poisson algebras starting with the more general concept of a Leibniz pair, namely of an associative algebra $A$ together with a Lie algebra $L$ mapped into the derivations of $A$. A…
In this paper, deformations of $L_\infty$-algebras are defined in such a way that the bases of deformations are $L_\infty$-algebras, as well. A universal and a semiuniversal deformation is constructed for $L_\infty$-algebras, whose…
In this article, we introduce a deformation cohomology of Leibniz superalgebras. Also, we introduce formal deformation theory of Leibniz superalgebras. Using deformation cohomology we study the formal deformation theory of Leibniz…
This paper develops the deformation theory of Lie ideals. It shows that the smooth deformations of an ideal $\mathfrak i$ in a Lie algebra $\mathfrak g$ differentiate to cohomology classes in the cohomology of $\mathfrak g$ with values in…
The deformation theory of Lie-Yamaguti algebras is developed by choosing a suitable cohomology. The relationship between the deformation and the obstruction of Lie-Yamaguti algebras is obtained.
Deformation Theory is a natural generalization of Lie Theory, from Lie groups and their linearization, Lie algebras, to differential graded Lie algebras and their higher order deformations, quantum groups. The article focuses on two basic…
The notion of quantum algebras is merged with that of Lie systems in order to establish a new formalism called Poisson-Hopf algebra deformations of Lie systems. The procedure can be naturally applied to Lie systems endowed with a symplectic…
The purpose of this paper is to extend the cohomology and conformal derivation theories of the classical Lie conformal algebras to Hom-Lie conformal algebras. In this paper, we develop cohomology theory of Hom-Lie conformal algebras and…
We study deformations of Lie groupoids by means of the cohomology which controls them. This cohomology turns out to provide an intrinsic model for the cohomology of a Lie groupoid with values in its adjoint representation. We prove several…
Generalising a previous work of Jiang and Sheng, a cohomology theory for differential Lie algebras of arbitrary weight is introduced. The underlying $L_\infty[1]$-structure on the cochain complex is also determined via a generalised version…
The purpose of this paper is to study Lie-Rinehart superalgebras over characteristic zero fields, which are consisting of a supercommutative associative superalgebra $A$ and a Lie superalgebra $L$ that are compatible in a certain way. We…
The purpose of this paper is to introduce an algebraic cohomology and formal deformation theory of left alternative algebras. Connections to some other algebraic structures are given also.
We consider deformations of finite or infinite dimensional Lie algebras over a field of characteristic 0. There is substantial confusion in the literature if one tries to describe all the non-equivalent deformations of a given Lie algebra.…