Related papers: Hom-algebras via PROPs
In many previous papers, the authors used an endomorphism of algebra to twist the original algebraic structures in order to produce the corresponding Hom-algebraic structures. In this works, we use these either a bijective linear map,…
The purpose of this paper is to study Sabinin algebras of Hom-type. It is shown that Lie, Malcev, Bol and other algebras of Hom-type are naturally Sabinin algebras of Hom-type. To this end, we provide a general key construction that…
The aim of this paper is to transfer the restrictedness theory to Hom-Lie algebras. The concept of restricted Hom-Lie algebras which is introduced in \cite{BM2} will be used in this paper. First, the existence of $p$-structures on a Hom-Lie…
(Multiplicative) Hom-Lie-Yamaguti superalgebras which generalize Hom-Lie supertriple systems (and subsequently ternary multiplicative Hom-Nambu superalgebras) and Hom-Lie superalgebras in the same way as Lie-Yamaguti superalgebras [Frac]…
Some basic properties of Hom-Leibniz algebras are found. These properties are the Hom-analogue of corresponding well-known properties of Leibniz algebras. Considering the Hom-Akivis algebra associated to a given Hom-Leibniz algebra, it is…
In this paper, first we discuss Hom-pre-Poisson algebras and their relationships with Hom-Poisson algebra. Then we introduce the notion of a Hom-pre-Gerstenhaber algebra and show that a Hom-pre-Gerstenhaber algebra gives rise to a…
We construct a PROP which encodes 2D-TQFTs with a grading. This defines a graded Frobenius algebra as algebras over this PROP. We also give a description of graded Frobenius algebras in terms of maps and relations. This structure naturally…
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, deformations, central extensions and derivation…
The notion of a $F$-manifold algebras is an algebraic description of a $F$-manifold. In this paper, we introduce the notion of Hom-$F$-manifold algebras which is generalisation of $F$-manifold algebras and Hom-Poisson algebras. We develop…
We study a twisted generalization of Novikov superalgebras, called Hom-Novikov superalgebras. It is shown that two classes of Hom-Novikov superalgebras can be constructed from Hom-supercommutative algebras together with derivations and…
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…
A twisting system is one of the major tools to study graded algebras, however, it is often difficult to construct a (non-algebraic) twisting system if a graded algebra is given by generators and relations. In this paper, we show that a…
We introduce the notion of relative averaging operators on Hom-associative algebras with a representation. Relative averaging operators are twisted generalizations of relative averaging operators on associative algebras. We give two…
In this paper, we define a new cohomology theory for multiplicative Hom-pre-Lie algebras which controls deformations of Hom-pre-Lie algebra structure. This new cohomology is a natural one by considering the structure map. We develop…
Hom-alternative and Hom-Jordan algebras are shown to give rise to Hom-Nambu algebras of arities 2^{k+1} + 1. The class of n-ary Hom-Maltsev algebras is studied. Multiplicative n-ary Hom-Nambu-Lie algebras are shown to be n-ary Hom-Maltsev…
Every multiplicative Hom-Malcev algebra has a natural multiplicative Hom-Lie triple system structure. Moreover, there is a natural Hom-Bol algebra structure on every multiplicative Hom-Malcev algebra and on every multiplicative right (or…
The main feature of Hom-algebras is that the identities defining the structures are twisted by linear maps. The purpose of this paper is to introduce and study a Hom-type generalization of pre-Malcev algebras, called Hom-pre-Malcev…
We introduce quasi-Hopf $*$-algebras i.e. quasi-Hopf algebras equipped with a conjugation (star) operation. The definition of quasi-Hopf $*$-algebras proposed ensures that the class of quasi-Hopf $*$-algebras is closed under twisting and…
In this paper, we consider compatible Hom-associative algebras as a twisted version of compatible associative algebras. Compatible Hom-associative algebras are characterized as Maurer-Cartan elements in a suitable bidifferential graded Lie…
The purpose of this paper is to extend the cohomology and conformal derivation theories of the classical Lie conformal algebras to Hom-Lie conformal algebras. In this paper, we develop cohomology theory of Hom-Lie conformal algebras and…