Related papers: On hom-Lie algebras
We show that the space R^n x gl(n,R) with a certain antisymmetric bracket operation contains all n-dimensional Lie algebras. The bracket does not satisfy the Jacobi identity, but it does satisfy it for subalgebras which are isotropic under…
A Lie algebra $L$ is said to be $(\Theta_{n},sl_{n})$-graded if it contains a simple subalgebra $\mathfrak{g}$ isomorphic to $sl_{n}$ such that the $\mathfrak{g}$-module $L$ decomposes into copies of the adjoint module, the trivial module,…
The aim of this paper is to introduce the notions of Hom Gel'fand-Dorfman bialgebra and Hom-Lie conformal algebra. In this paper, we give four constructions of Hom Gel'fand-Dorfman bialgebras. Also, we provide a general construction of…
In this paper, the Hom-Lie superalgebra structures on exceptional simple Lie superalgebras of vector fields are studied. Taking advantage of the Z-grading structures and the transitivity, we prove that there is only the trivial Hom-Lie…
In this paper, first we modify the definition of a Hom-Lie algebroid introduced by Laurent-Gengoux and Teles and give its equivalent dual description. Many results that parallel to Lie algebroids are given. In particular, we give the notion…
We construct Quillen equivalent semi-model structures on the categories of dg-Lie algebroids and $L_\infty$-algebroids over a commutative dg-algebra in characteristic zero. This allows one to apply the usual methods of homotopical algebra…
We introduce hom-Lie-Rinehart algebras as an algebraic analogue of hom-Lie algebroids, and systematically describe a cohomology complex by considering coefficient modules. We define the notion of extensions for hom-Lie-Rinehart algebras. In…
The aim of this paper is to compare the structure and the cohomology spaces of Lie algebras and induced $3$-Lie algebras.
In this paper, we study Hom-Lie bialgebras by a new notion of the dual representation of a representation of a Hom-Lie algebra. Motivated by the essential connection between Lie bialgebras and Manin triples, we introduce the notion of a…
We consider algebras over a field $k$ of characteristic zero. The article is concerned with the isomorphism of graded vectorspaces \[ H(\gl(A))\iso\wedge (HC(A)[-1]) \] between the Lie algebra homology of matrices and the free graded…
A coassociative Lie algebra is a Lie algebra equipped with a coassociative coalgebra structure satisfying a compatibility condition. The enveloping algebra of a coassociative Lie algebra can be viewed as a coalgebraic deformation of the…
Quantum Lie algebras are generalizations of Lie algebras whose structure constants are power series in $h$. They are derived from the quantized enveloping algebras $\uqg$. The quantum Lie bracket satisfies a generalization of antisymmetry.…
In two seminal papers M. Kontsevich introduced graph homology as a tool to compute the homology of three infinite dimensional Lie algebras, associated to the three operads `commutative,' `associative' and `Lie.' We generalize his theorem to…
The notion of an F-manifold algebra is the underlying algebraic structure of an $F$-manifold. We introduce the notion of pre-Lie formal deformations of commutative associative algebras and show that F-manifold algebras are the corresponding…
In this paper, we first introduce the notion of Hom-left-symmetric conformal bialgebras and show some nontrivial examples. Also, we present construction methods of matched pairs of Hom-Lie conformal algebras and Hom-left-symmetric conformal…
In this paper, we introduce the notions of pseudo-Riemannian, para-Hermitian and para- Kahler structures on hom-Lie algebras. In addition, we present the characterization of these structures. Also, we provide an example including these…
In these notes, we introduce formal hom-associative deformations of the quantum planes and the universal enveloping algebras of the two-dimensional non-abelian Lie algebras. We then show that these deformations induce formal hom-Lie…
In this paper, we study the double extension of a restricted quadratic Hom-Lie algebra $(V,[\cdot,\cdot]_{V},\alpha_{V},B_{V})$, which is an enlargement of $V$ by means of a central extension and a restricted derivation $\mathscr{D}$. In…
Nongraded infinite-dimensional Lie algebras appeared naturally in the theory of Hamiltonian operators, the theory of vertex algebras and their multi-variable analogues. They play important roles in mathematical physics. This survey article…
We introduce the notions of pre-morphism and pre-derivation for arbitrary non-associative algebras over a commutative ring $k$ with identity. These notions are applied to the study of pre-Lie $k$-algebras and, more generally, Lie-admissible…