Related papers: Hom-power associative algebras
This paper is mainly devoted to a structure study of Hom-alternative algebras . Equivalent conditions for Hom-alternative algebras being solvable, simple and semi-simple are displayed. Moreover some results about Hom-alternative bimodule…
From the definition and properties of unital hom-associative algebras, and the use of the Kaplansky's constructions, we develop new algebraic structures called 2-hom-associative bialgebras, 2-hom-bialgebras, and 2-2-hom-bialgebras. Besides,…
The three-algebras used by Bagger and Lambert in N=6 theories of ABJM type are in one-to-one correspondence with a certain type of Lie superalgebras. We show that the description of three-algebras as generalized Jordan triple systems…
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…
In hom-associative structures, the associativity condition $(xy)z=x(yz)$ is twisted to $\alpha(x)(yz) = (xy)\alpha(z)$, with $\alpha$ a map in the appropriate category. In the present paper, we consider two different unitality conditions…
In this paper, we introduce the notion of algebras of quotients of Hom-Lie algebras and investigate some properties which can be lifted from a Hom-Lie algebra to its algebra of quotients. We also give some necessary and sufficient…
We study algebras $A,$ over a field of characteristic zero, satisfying $(x^p, x^q, x^r)=0$ for $p, q, r$ in ${1, 2}.$ The existence of a unit element in such algebras leads to the third power-associativity. If, in addition, $A$ has degree…
By applying a recent construction of free Baxter algebras, we obtain a new class of Hopf algebras that generalizes the classical divided power Hopf algebra. We also study conditions under which these Hopf algebras are isomorphic.
Representations of color Hom-Lie algebras are reviewed, and it is shown that there exist a series of coboundary operators. We also introduce the notion of a color omni-Hom-Lie algebra associated to a vector space and an even invertible…
In this paper, we define and study (co)homology theories of a compatible associative algebra $A$. At first, we construct a new graded Lie algebra whose Maurer-Cartan elements are given by compatible associative structures. Then we define…
The paper is devoted to the study of evolution algebras that are power-associative algebras. We give the Wedderburn decomposition of evolution algebras that are power-associative algebras and we prove that these algebras are Jordan…
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 study Hom-type analogs of Rota-Baxter and dendriform algebras, called Rota-Baxter $G$-Hom-associative algebras and Hom-dendriform algebras. Several construction results are proved. Free algebras for these objects are explicitly…
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…
Given a vector space with two multiplications, one commutative the other anticommutative, possibly connected by a distributive law, the depolarization principle allows to look at this triplet through a single nonassociative multiplication.…
In quantum mechanics, associative algebras play an important role in understanding symmetries and operator algebras, providing new algebraic frameworks for describing physical systems. This work classifies associative algebras over a field…
(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]…
This paper addresses the classification problem of associative algebras over arbitrary base fields. We present a list of three-dimensional associative algebras with canonical representatives of the isomorphism classes for fields of…
A hom-associative algebra is an algebra whose associativity is twisted by an algebra homomorphism. We show that the Hochschild type cochain complex of a hom-associative algebra carries a homotopy G-algebra structure. As a consequence, we…
For an associative algebra $A$ a skew-symmetric sum of $n!$ products of $n$ elements of $A$ in all possible order is called $n$-commutator. We consider $A$ as $n$-ary algebra under $n$-commutator. We prove that it has an identity of…