The main feature of Hom-algebras is that the identities defining structures are twisted by linear maps. purpose this paper to introduce and study a Hom-type generalization pre-Malcev algebras, called Hom-pre-Malcev algebras. We also notion Kupershmidt operators Hom-Malcev algebras show connections between using operators. generalize Hom-pre-Lie Hom-alternative setting fit into bigger framework ...

The purpose of this paper is to study Sabinin algebras Hom-type. It shown that Lie, Malcev, Bol and other Hom-type are naturally To end, we provide a general key construction establish relationship between identities some class Hom-algebras ordinary algebras. Moreover, discuss new concept Hom-bialgebra, in relation with universal enveloping Hom-algebras. A based on primitive elements provided.

This paper is devoted to the construction of Hom-Leibniz H-pseudoalgebras, which unify Hom-Lie Leibniz H-pseudoalgebras and algebras. Firstly, we give theorem obtain a class H-pseudoalgebras. We also construct Hom- from different perspectives, including (resp. Hom-Lie, Hom-associative) their representations, Homassociative) Thenwegive some properties representations Hom-LeibnizH-pseudoalgebras....

The aim of this work is to introduce and study the notions Hom-pre-Jordan algebra Hom-J-dendriform which generalize Hom-Jordan algebras. algebras are regarded as underlying algebraic structures behind Rota-Baxter operators O-operators introduced in paper. also analogues Hom-pre-Lie for anti-commutator a left multiplication operator gives representation algebra. On other hand, analogue Hom-dendr...

Summary We formalize in the Mizar system [3], [4] some basic properties on left module over a ring such as constructing via of endomorphism an abelian group and set all homomorphisms modules form [1] along with Ch. 2 set. 1 [2]. The formalized items are shown below list notations: M ab for Abelian suffix “ ” without is used ring. 1. denoted by End ( ). 2. A pair homomorphism <m:math xmlns:m="ht...

We introduce a Hom-type generalization of quantum groups, called quasi-triangular Hom-bialgebras. They are non-associative and non-coassociative analogues of Drinfel’d’s quasitriangular bialgebras, in which the non-(co)associativity is controlled by a twisting map. A family of quasi-triangular Hom-bialgebras can be constructed from any quasi-triangular bialgebra, such as Drinfel’d’s quantum env...

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...

This paper studies homogeneously Suslin (hom) sets of reals in tame mice. The following results are established: In 0¶ the hom sets are precisely the ̃ 11 sets. In Mn every hom set is correctly ̃ 1n+1, and (δ + 1)-universally Baire where δ is the least Woodin. In Mω every hom set is <λ-hom, where λ is the supremum of the Woodins. §

Given a nite dimensional algebra over an algebraically closed eld one frequently disregards the projective objects in the category mod of nite dimensional-modules and focuses on the stable category mod. The objects of mod are those of mod but the Hom-groups are the ordinary Hom-groups modulo the subgroup of those morphisms which factor through a projective-module. In this paper we show that mod...