Related papers: On unitality conditions for Hom-associative algebr…
We study Hom-bialgebras and objects admitting coactions by Hom-bialgebras. In particular, we construct a Hom-bialgebra M representing the functor of 2x2-matrices on Hom-associative algebras. Then we construct a Hom-algebra analogue of the…
This paper introduces Hom-type analogues of affine algebraic structures, termed Hom-affgebras. Extending Brzezi\'nski's theory of affgebras and the Hom-algebra framework developed by Hartwig-Larsson-Silvestrov, we define and study…
The purpose of this paper is to define an $\alpha$-type cohomology, which we call $\alpha$-type Chevalley-Eilenberg cohomology, for Hom-Lie algebras. We relate it to the known Chevalley-Eilenberg cohomology and provide explicit computations…
In this paper we find some necessary and sufficient conditions for a Banach algebra to be amenable or weakly amenable, by applying the homomorphisms on Banach 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…
In this paper, we introduce two types of deformation maps of quasi-twilled associative algebras. Each type of deformation maps unify various operators on associative algebras. Right deformation maps unify modified Rota-Baxter operators of…
For A a separable unital C*-algebra and M a separable McDuff II_1-factor, we show that the space Hom_w(A,M) of weak approximate unitary equivalence classes of unital *-homomorphisms A \rightarrow M may be considered as a closed, bounded,…
A twisted generalization of Lie-Yamaguti algebras, called Hom-Lie-Yamaguti algebras, is defined. Hom-Lie-Yamaguti algebras generalize Hom-Lie triple systems (and susequently ternary Hom-Nambu algebras) and Hom-Lie algebras in the same way…
Hom-Bol algebras are defined as a twisted generalization of (left) Bol algebras. Hom-Bol algebras generalize multiplicative Hom-Lie triple systems in the same way as Bol algebras generalize Lie triple systems. The notion of an $n$th derived…
A quasi-twilled associative algebra is an associative algebra $\mathbb{A}$ whose underlying vector space has a decomposition $\mathbb{A} = A \oplus B$ such that $B \subset \mathbb{A}$ is a subalgebra. In the first part of this paper, we…
In this paper, we first define twisted Rota-Baxter family operators on Hom-associative algebras indexed by a semigroup $\Omega$. Then we introduce and study Hom-NS-family algebras as the underlying structures of twisted Rota-Baxter family…
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…
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…
This article is devoted to the investigation of the deformation (twisting) of monoidal structures, such as the associativity constraint of the monoidal category and the monoidal structure of monoidal functor. The sets of twistings have a…
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…
Hom-structures (Lie algebras, algebras, coalgebras, Hopf algebras) have been investigated in the literature recently. We study Hom-structures from the point of view of monoidal categories; in particular, we introduce a symmetric monoidal…
Let $A$ be a Banach algebra and $X$ be a compact Hausdorff space. Given homomorphisms $ \sigma \in Hom(A)$ and $\tau \in Hom(C(X, A))$, we introduce induced homomorphisms $\tilde{\sigma}\in Hom(C(X, A)) $ and $\tilde{\tau}\in Hom(A)$,…
In the recent definition of Hom-Hopf algebras the antipode S is the relative Hominverse of the identity map with respect to the convolution product. We observe that some fundamental properties of the antipode of Hopf algebras and Hom-Hopf…
We define a new cohomology for associative algebras which we compute for algebras with units.
We introduce and study a $K$-theory of twisted bundles for associative algebras $A(\mathfrak g)$ of formal series with an infinite-Lie algebra coefficients over arbitrary compact topological spaces. Fibers of such bundles are given by…