Related papers: Right Hom-alternative algebras
We develop the theory dg algebras with enough idempotents and their dg modules and show their equivalence with that of small dg categories and their dg modules. We introduce the concept of dg adjunction and show that the classical covariant…
The aim of this paper is to introduce the notion of restricted Hom- Lie superalgebras. This class of algebras is a generalization of both restricted Hom-Lie algebras and restricted Lie superalgebras. In this paper, we present a way to…
The purpose of this paper is to study deformation theory of Hom-associative algebra morphisms and Hom-Lie algebra morphisms. We introduce a suitable cohomology and discuss Infinitesimal deformations, equivalent deformations and…
Hom-quadri dendriform algebras and Hom-six-dendriform agebras are introduced and studied which is a splitting of a Hom-diassociative and Hom-triassociative algebras, respectively. Moreover we explore the connections be tween these…
An algebra $A$ with identity $(a\circ b)\circ c-a\circ(b\circ c)=(a\circ c)\circ b-a\circ(c\circ b),$ is called right-symmetric. Cohomology and deformation theory for right-symmetric algebras are developed. Cohomologies of $gl_n$ and…
There are many contexts in algebraic geometry, algebraic topology, and homological algebra where one encounters a functor that has both a left and right adjoint, with the right adjoint being isomorphic to a shift of the left adjoint…
In this paper, we present and explore several key concepts within the framework of Hom-Poisson algebras. Specifically, we introduce the notions of admissible Hom-Poisson algebras, along with the related ideas of matched pairs and Manin…
In this paper we give an attempt to extend some arithmetic properties such as multiplicativity, convolution products to the setting of operators theory. We provide a significant examples which are of interest in number theory. We also give…
There is a relatively well-known description of the algebra of (higher order) left differential operators on commutative algebras. This note gives a construction of similar flavor for algebras of differential operators on not necessarily…
A structure of a left-symmetric algebra on the set of all derivations of a free algebra is introduced such that its commutator algebra becomes the usual Lie algebra of derivations. Left and right nilpotent elements of left-symmetric…
A Hom-group G is a nonassociative version of a group where associativity, invertibility, and unitality are twisted by a map \alpha: G\longrightarrow G. Introducing the Hom-group algebra KG, we observe that Hom-groups are providing examples…
This paper introduces the notion of Hom-Lie color algebra, which is a natural general- ization of Hom-Lie (super)algebras. Hom-Lie color algebras include also as special cases Lie (super) algebras and Lie color algebras. We study the…
In this work, the hom-center-symmetric algebras are constructed and discussed. Their bimodules, dual bimodules and matched pairs are defined. The relation between the dual bimodules of hom-center-symmetric algebras and the matched pairs of…
We develop a structure theory for nilpotent symplectic alternating algebras. We then give a classification of all nilpotent symplectic alternating algebras of dimension up to 10 over any field. The study reveals a new subclasses of powerful…
The main purpose of this paper is to provide a full cohomology of a Hom-pre-Lie algebra with coefficients in a given representation. This new type of cohomology exploit strongly the Hom-type structure and fits perfectly with simultaneous…
The purpose of this paper is to introduce an algebraic cohomology and formal deformation theory of left alternative algebras. Connections to some other algebraic structures are given also.
In this paper, we consider compatible Hom-Leibniz algebra where the Hom map twists the operations in the compatible system. We consider a suitably graded Lie algebra whose Maurer-Cartan elements characterize the structure of compatible…
The aim of this paper is to introduce and study Rota-Baxter Hom-algebras. Moreover we introduce a generalization of the dendriform algebras and tridendriform algebras by twisting the identities by mean of a linear map. Then we explore the…
On Hom-Lie algebras and superalgebras,we introduce the notions of biderivations, linear commuting maps and {\alpha}-biderivations, and compute them for some typical Hom-Lie algebras and superalgebras, including q-deformed W(2,2) algebra,…
The aim of this paper is to present remarkable classes of Lie-admissible algebras containing in particular the associative algebras, the Vinberg algebras and pre-Lie algebras. We determine the associated quadratic operads and their dual…