Related papers: Hom-bialgebras and comodule Hom-algebras
We classify, up to isomorphism, the 2-dimensional algebras over a field K. We focuse also on the case of characteristic 2, identifying the matrices of GL(2,F_2) with the elements of the symmetric group S_3. The classification is then given…
In this article, we use the theory of (non-abelian) exterior product of Hom-Lie algebras to prove the Hopf formula for these algebras. As an application, we construct an eight-term sequence in the homology of Hom-Lie algebras. We also…
Aim of this paper is to define a new type of cohomology for multiplicative Hom-Leibniz algebras which controls deformations of Hom-Leibniz algebra structure. The cohomology and the associated deformation theory for Hom-Leibniz algebras as…
It shown that the supercommutator superalgebra of a right alternative superalgebra is a Bol superalgebra. Hom-Bol superalgebras are defined and it is shown that they are closed under even self-morphisms. Any Bol superalgebra along with any…
A Hom-type algebra is called involutive if its Hom map is multiplicative and involutive. In this paper, we obtain an explicit construction of the free involutive Hom-associative algebra on a Hom-module. We then apply this construction to…
This contribution studies a specific deformation of algebras with anti-involution. Starting with the observation that twisting the multiplication of such an algebra by its anti-involution generates a Hom-associative algebra of type II, it…
In this work, the partially and totally hom-coassociative ternary coalgebras are constructed and discussed. Their {infinitesimal} bialgebraic structures are also investigated. The related dual space structures and their properties are…
In this paper, first we study dual representations and tensor representations of Hom-pre-Lie algebras. Then we develop the cohomology theory of Hom-pre-Lie algebras in term of the cohomology theory of Hom-Lie algebras. As applications, we…
A BiHom-associative algebra is a (nonassociative) algebra $A$ endowed with two commuting multiplicative linear maps $\alpha,\beta\colon A\rightarrow A$ such that $\alpha (a)(bc)=(ab)\beta (c)$, for all $a, b, c\in A$. This concept arose in…
In this paper, we introduce a new definition of a hom-Lie bialgebra, which is equivalent to a Manin triple of hom-Lie algebras. We also introduce a notion of an $\mathcal O$-operator and then construct solutions of the classical…
An internal coproduct is described, which is compatible with Hoffman's quasi-shuffle product. Hoffman's quasi-shuffle Hopf algebra, with deconcatenation coproduct, is a comodule-Hopf algebra over the bialgebra thus defined. The relation…
We introduce the new concept of braided Hom-Lie bialgebras which is a generalization of Sommerh\"{a}user-Majid's braided Lie bialgebras and Yau's Hom-Lie bialgebras. Using this concept we give the unified product construction for Hom-Lie…
Several recent results concerning Hom-Leibniz algebra are reviewed, the notion of symmetric Hom-Leibniz superalgebra is introduced and some properties are obtained. Classification of 2-dimensional Hom-Leibniz algebras is provided. Centroids…
We describe Hom-Lie structures on affine Kac-Moody and related Lie algebras, and discuss the question when they form a Jordan algebra.
It is shown that every n-ary totally Hom-associative algebra with equal twisting maps yields an n-ary Hom-Nambu algebra via an n-ary version of the commutator bracket. The class of n-ary totally Hom-associative algebras is shown to be…
The aim of this paper is to generalize the concept of Lie-admissible coalgebra introduced by Goze and Remm to Hom-coalgebras and to introduce Hom-Hopf algebras with some properties. These structures are based on the Hom-algebra structures…
Hom-Akivis algebras are introduced. The commutator-Hom-associator algebra of a non-Hom-associative algebra (i.e. a Hom-nonassociative algebra) is a Hom-Akivis algebra. It is shown that non-Hom-associative algebras can be obtained from…
We introduce the first hom-associative Weyl algebras over a field of prime characteristic as a generalization of the first associative Weyl algebra in prime characteristic. First, we study properties of hom-associative algebras constructed…
Hom-bialgebras and Hom-Hopf algebras are generalizations of bialgebra and Hopf algebra structures, where associativity and coassociativity conditions are twisted by a homomorphism. The purpose of this paper is to define a…
We introduce the concept of Hom-associative algebra structures in Loday-Pirashvili category.The cohomology theory of Hom-associative algebras in this category is studied.Some applications on deformation and abelian extension theory are…