Universal imbedding of a Hom-Lie Triple System
نویسنده
چکیده
In this article we will build a universal imbedding of a regular HomLie triple system into a Lie algebra and show that the category of regular Hom-Lie triple systems is equivalent to a full subcategory of pairs of Z2graded Lie algebras and Lie algebra automorphism, then finally give some characterizations of this subcategory.
منابع مشابه
Enveloping Algebras of Hom-lie Algebras
A Hom-Lie algebra is a triple (L, [−,−], α), where α is a linear self-map, in which the skew-symmetric bracket satisfies an α-twisted variant of the Jacobi identity, called the Hom-Jacobi identity. When α is the identity map, the Hom-Jacobi identity reduces to the usual Jacobi identity, and L is a Lie algebra. Hom-Lie algebras and related algebras were introduced in [1] to construct deformation...
متن کاملOn universal central extensions of Hom-Leibniz algebras
In the category of Hom-Leibniz algebras we introduce the notion of Hom-corepresentation as adequate coefficients to construct the chain complex from which we compute the Leibniz homology of Hom-Leibniz algebras. We study universal central extensions of Hom-Leibniz algebras and generalize some classical results, nevertheless it is necessary to introduce new notions of α-central extension, univer...
متن کاملIdeals in Non-associative Universal Enveloping Algebras of Lie Triple Systems
The notion of a non-associative universal enveloping algebra for a Lie triple system arises when Lie triple systems are considered as Bol algebras (more generally, Sabinin algebras). In this paper a new construction for these universal enveloping algebras is given, and their properties are studied. It is shown that universal enveloping algebras of Lie triple systems have surprisingly few ideals...
متن کاملHom-alternative Algebras and Hom-jordan Algebras
The purpose of this paper is to introduce Hom-alternative algebras and Hom-Jordan algebras. We discuss some of their properties and provide construction procedures using ordinary alternative algebras or Jordan algebras. Also, we show that a polarization of Hom-associative algebra leads to Hom-Jordan algebra. INTRODUCTION Hom-algebraic structures are algebras where the identities defining the st...
متن کاملRight ideals in non–associative universal enveloping algebras of Lie triple systems
We prove that the only proper right ideal of the universal enveloping algebra of a finite–dimensional central simple Lie triple system over a field of characteristic zero is its augmentation ideal.
متن کامل