Enveloping algebras of Hom-Lie algebras

  title={Enveloping algebras of Hom-Lie algebras},
  author={Donald Yau},
  journal={Journal of Generalized Lie Theory and Applications},
  • Donald Yau
  • Published 6 September 2007
  • Mathematics
  • Journal of Generalized Lie Theory and Applications
Enveloping algebras of Hom-Lie and Hom-Leibniz algebras are constructed. 2000 MSC: 05C05, 17A30, 17A32, 17A50, 17B01, 17B35, 17D25 1 
Hom-Algebras and Homology
Classes of G -Hom-associative algebras are constructed as deformations of G -associative algebras along algebra endomorphisms. As special cases, we obtain Hom-associative and Hom-Lie algebras as
Hom-algebras via PROPs
Hom-algebras over a PROP are defined and studied. Several twisting constructions for Hom-algebras over a large class of PROPs are proved, generalizing many such results in the literature. Partial
Module Hom-algebras
We study a twisted version of module algebras called module Hom-algebras. It is shown that module algebras deform into module Hom-algebras via endomorphisms. As an example, we construct certain
Restricted hom-Lie algebras
The paper studies the structure of restricted hom-Lie algebras. More specifically speaking, we first give the equivalent definition of restricted hom-Lie algebras. Second, we obtain some properties
Representations of Hom-Lie Algebras
In this paper, we study representations of hom-Lie algebras. In particular, the adjoint representation and the trivial representation of hom-Lie algebras are studied in detail. Derivations,
HNN-extension of involutive multiplicative Hom-Lie algebras
The construction of HNN-extensions of involutive Hom-associative algebras and involutive Hom-Lie algebras is described. Then, as an application of HNN-extension, by using the validity of
On (n+1)-Hom-Lie algebras induced by n-Hom-Lie algebras
Abstract The purpose of this paper is to study the relationships between an n-Hom-Lie algebra and its induced (n+1)-Hom-Lie algebra. We provide an overview of the theory and explore structure
Some remarks on Hom-modules and Hom-path algebras
This paper deals with injective and projective right Hom-H-modules for a Hom-algebra H. In particular, Baer Criterion of injective Hom-module is obtained, and it is shown that HomModH is an Abelian
Hom-bialgebras and Comodule Algebras
We construct a Hom-bialgebra M(2) representing the functor of 2 × 2-matrices on Hom-associative algebras. We also construct a Hom-algebra analogue of the affine plane and show that it is a comodule
Morphisms Cohomology and Deformations of Hom-algebras
The purpose of this paper is to define cohomology complexes and study deformation theory of Hom-associative algebra morphisms and Hom-Lie algebra morphisms. We discuss infinitesimal deformations,


On Hom-algebra structures
A Hom-algebra structure is a multiplication on a vector space where the structure is twisted by a homomorphism. The structure of Hom-Lie algebra was introduced by Hartwig, Larsson and Silvestrov and
Dialgebras and Related Operads
Dialgebras.- Dialgebra (co)homology with coefficients.- Un endofoncteur de la categorie des operades.- Un theoreme de Milnor-Moore pour les algebres de Leibniz.
Deformations of Lie Algebras using σ-Derivations
Universal enveloping algebras of Leibniz algebras and (co)homology
The homology of Lie algebras is closely related to the cyclic homology of associative algebras [LQ]. In [L] the first author constructed a "noncommutative" analog of Lie algebra homology which is,
AbstractWe equip the category $$\mathcal{L}\mathcal{M}$$ of linear maps of vector spaces with a tensor product which makes it suitable for various constructions related to Leibniz algebras. In
Une version non commutative des algèbres de Lie : les algèbres de Leibniz
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