A Non-abelian Tensor Product of Hom–Lie Algebras

@article{Casas2014ANT,
  title={A Non-abelian Tensor Product of Hom–Lie Algebras},
  author={Jos{\'e} Manuel Casas and Emzar Khmaladze and N. Pacheco Rego},
  journal={Bulletin of the Malaysian Mathematical Sciences Society},
  year={2014},
  volume={40},
  pages={1035-1054}
}
Non-abelian tensor product of Hom–Lie algebras is constructed and studied. This tensor product is used to describe universal ($$\alpha $$α)-central extensions of Hom–Lie algebras and to establish a relation between cyclic and Milnor cyclic homologies of Hom-associative algebras satisfying certain additional condition. 
View on Springer
arxiv.org
14 Citations
Background Citations
5
Methods Citations
3

14 Citations

Citation Type

Citation Type

A non-abelian Hom-Leibniz tensor product and applications
Abstract The notion of non-abelian Hom–Leibniz tensor product is introduced and some properties are established. This tensor product is used in the description of the universal (-)central extensions…
A non-abelian exterior product of Hom-Leibniz algebras
In this paper, we introduce a non-abelian exterior product of Hom-Leibniz algebras and investigate its relative to the Hopf’s formula. We also construct an eight-term exact sequence in the homology…
On some properties preserved by the non-abelian tensor product of Hom-Lie algebras
ABSTRACT We study some properties of the non-abelian tensor product of Hom-Lie algebras concerning the preservation of products and quotients, solvability and nilpotency, and describe compatibility…
The exterior product and homology of Hom-Lie algebras
In this article, we use the theory of (non-abelian) exterior product of Hom-Lie algebras to prove the Hopf’s formula for these algebras. As an application, we construct an eight-term sequence in the…
Universal central extensions and non-abelian tensor product of hom-Lie–Rinehart algebras
In this paper we study universal central extensions and non-abelian tensor product of hom-Lie-Rinehart algebras. We discuss about universal $\alpha$- central extensions, and, lifting of automorphisms…
Universal central extensions of Lie–Rinehart algebras
In this paper, we study the universal central extension of a Lie–Rinehart algebra and we give a description of it. Then we study the lifting of automorphisms and derivations to central extensions. We…
On the Capability of Hom-Lie Algebras
A Hom-Lie algebra pL, αLq is said to be capable if there exists a Hom-Lie algebra pH,αH q such that L – H{ZpHq. We obtain a characterisation of capable Hom-Lie algebras involving its epicentre and we…
Cohomology characterizations of non-abelian extensions of Hom-Lie algebras
In this paper, first we show that under the assumption of the center of h being zero, diagonal non-abelian extensions of a regular Hom-Lie algebra g by a regular Hom-Lie algebra h are in one-to-one…
Cohomology Characterizations of Diagonal Non-Abelian Extensions of Regular Hom-Lie Algebras
In this paper, first we show that under the assumption of the center of h being zero, diagonal non-abelian extensions of a regular Hom-Lie algebra g by a regular Hom-Lie algebra h are in one-to-one…
Hom-Lie-Rinehart algebras
ABSTRACT 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…
...
...

References

SHOWING 1-10 OF 21 REFERENCES
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…
NON-ABELIAN HOMOLOGY OF LIE ALGEBRAS
Non-abelian homology of Lie algebras with coefficients in Lie algebras is constructed and studied, generalising the classical Chevalley-Eilenberg homology of Lie algebras. The relationship between…
Hom-Lie algebra structures on semi-simple Lie algebras
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,…
Notes on 1-parameter formal deformations of Hom-associative and Hom-Lie algebras
Abstract The aim of this paper is to extend to Hom-algebra structures the theory of 1-parameter formal deformations of algebras which was introduced by Gerstenhaber for associative algebras and…
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…
Enveloping algebras of Hom-Lie algebras
Enveloping algebras of Hom-Lie and Hom-Leibniz algebras are constructed. 2000 MSC: 05C05, 17A30, 17A32, 17A50, 17B01, 17B35, 17D25 1
On universal central extensions of Hom-Lie algebras
We develop a theory of universal central extensions of Hom-Lie algebras. Classical results of universal central extensions of Lie algebras cannot be completely extended to Hom-Lie algebras setting,…
Universal Central Extensions in Semi-Abelian Categories
TLDR
A new fundamental condition on composition of central extensions is considered and examples of categories which do, or do not, satisfy this condition are given.
Deformations of Lie Algebras using σ-Derivations
...
...