Related papers: Algebra Structures on Hom(C,L)
We study hom-associative structures on general possibly non-associative algebras focusing on one-sided and two-sided unital algebras. New characterizations and aspects of these structures, along with some important subclasses, are explored…
We study and classify the 3-dimensional Hom-Lie algebras over $\mathbb{C}$. We provide first a complete set of representatives for the isomorphism classes of skew-symmetric bilinear products defined on a 3-dimensional complex vector space…
We study Chevalley-Eilenberg cohomology of physically relevant Lie superalgebras related to supersymmetric theories, providing explicit expressions for their cocycles in terms of their Maurer-Cartan forms. We then include integral forms in…
The purpose of this paper is to introduce twisted $\mathcal{O}$-operators on $3$-Lie algebras. We define a cohomology of a twisted $\mathcal{O}$-operator $T$ as the Chevalley-Eilenberg cohomology of a certain $3$-Lie algebra induced by $T$…
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…
We show that the Heisenberg Lie algebras over a field $\mathbb{F}$ of characteristic $p>0$ admit a family of restricted Lie algebras, and we classify all such non-isomorphic restricted Lie algebra structures. We use the ordinary 1- and…
We investigate restricted Lie algebras arising as analogues of (twisted) right-angled Artin groups and right-angled Coxeter groups over fields of characteristic two. These algebras are defined via quadratic relations determined by decorated…
The aim of this paper is to define and study Drinfeld twists for monoidal Hom-bialgebras. We show that a new Hom-bialgebra could be constructed by changing the coproduct of a monoidal Hom-bialgebra via a Drinfeld twist, and this…
In this paper, we consider compatible Hom-Lie algebras as a twisted version of compatible Lie algebras. Compatible Hom-Lie algebras are characterized as Maurer-Cartan elements in a suitable bidifferential graded Lie algebra. We also define…
We survey decades of research identifying the (co)homology of configuration spaces with Lie algebra (co)homology. The different routes to this one proto-theorem offer genuinely different explanations of its truth, and we attempt to convey…
A hom-associative structure is a set $A$ together with a binary operation $\star$ and a selfmap $\alpha$ such that an $\alpha$-twisted version of associativity is fulfilled. In this paper, we assume that $\alpha$ is surjective. We show that…
In this paper, first using the higher derived brackets, we give the controlling algebra of relative difference Lie algebras, which are also called crossed homomorphisms or differential Lie algebras of weight 1 when the action is the adjoint…
For the associative algebra $A(\mathfrak g)$ of an infinite-dimensional Lie algebra $\mathfrak g$, we introduce twisted fiber bundles over arbitrary compact topological spaces. Fibers of such bundles are given by elements of algebraic…
We show that the higher-order Weyl algebras over a field of characteristic zero, which are formally rigid as associative algebras, can be formally deformed in a nontrivial way as hom-associative algebras. We also show that these…
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…
We define closed model category structures on different categories connected to the world of operad algebras over the category C(k) of (unbounded) complexes of k-modules: on the category of operads, on the category of algebras over a fixed…
Hom-dendriform algebras are twisted analog of dendriform algebras and are splitting of hom-associative algebras. In this paper, we define a cohomology and deformation for hom-dendriform algebras. We relate this cohomology with the…
The $A(\inft)$-algebra structure in homology of a DG-algebra is constructed. This structure is unique up to isomorphism of $A(\infty)$ algebras. Connection of this structure with Massey products is indicated. The notion of…
We study cohomology theories of strongly homotopy algebras, namely $A_\infty, C_\infty$ and $L_\infty$-algebras and establish the Hodge decomposition of Hochschild and cyclic cohomology of $C_\infty$-algebras thus generalising previous work…
Adapting the idea of twisted tensor products to the category of finitely generated algebras, we define on its opposite, the category QLS of quantum linear spaces, a family of objects hom(B,A)^{op}, one for each pair A^{op},B^{op} there,…