Related papers: Module Hom-algebras
In this paper we introduce modules over both left and right Hom-alternative algebras. We give some constructions of left and right Hom-alternative modules and give various properties of both, as well as examples. Then, we prove that…
We classify hom-Lie structures with nilpotent twisting map on $3$-dimensional complex Lie algebras, up to isomorphism, and classify all degenerations in such family. The ideas and techniques presented here can be easily extrapolated to…
We construct a family of exact functors from the BGG category of representations of the Lie algebra sl to the category of finite-dimensional representations of the degenerate (or graded) affine Hecke algebra H of GL. These functors…
Degeneration of modules is usually defined geometrically, but due to results of Zwara and Riedtmann we can also define it in terms of exact sequences. This definition also works over fields that are not algebraically closed. Let $k$ be a…
We study endomorphism algebras of 2-term silting complexes in derived categories of hereditary finite dimensional algebras, or more generally of $\mathop{\rm Ext}\nolimits$-finite hereditary abelian categories. Module categories of such…
A Hom-algebra structure is a multiplication on a vector space where the structure is twisted by a homomorphism. The structure of Hom-Lie algebra was introduced by Hartwig, Larsson and Silvestrov and extended by Larsson and Silvestrov to…
We introduce the notion of 3-Hom-Lie-Rinehart algebra and systematically describe a cohomology complex by considering coefficient modules. Furthermore, we consider extensions of a 3-Hom-Lie-Rinehart algebra and characterize the first…
Motivated by logarithmic conformal field theory and Gromov-Witten theory, we introduce a notion of a twisted module of a vertex algebra under an arbitrary (not necessarily semisimple) automorphism. Its main feature is that the twisted…
We study vertex algebras and their modules associated with possibly degenerate even lattices, using an approach somewhat different from others. Several known results are recovered and a number of new results are obtained. We also study…
We consider the space of linear maps from a coassociative coalgebra C into a Lie algebra L. Unless C has a cocommutative coproduct, the usual symmetry properties of the induced bracket on Hom(C,L) fail to hold. We define the concept of…
On Hom-Lie algebras and superalgebras,we introduce the notions of biderivations, linear commuting maps and {\alpha}-biderivations, and compute them for some typical Hom-Lie algebras and superalgebras, including q-deformed W(2,2) algebra,…
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…
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…
Motivated by recent work on Hom-Lie algebras, a twisted version of the Yang-Baxter equation, called the Hom-Yang-Baxter equation (HYBE), was introduced by the author in an earlier paper. In this paper, several more classes of solutions of…
In the present paper we investigate the noncommutative geometry of a class of algebras, called the Hom-associative algebras, whose associativity is twisted by a homomorphism. We define the Hochschild, cyclic, and periodic cyclic homology…
Hom-Lie superalgebras, which can be considered as a deformation of Lie superalgebras, are $\mathbb{Z}_2$-graded generalization of Hom-Lie algebras. In this paper, we prove that there is only the trivial Hom-Lie superalgebra structure over a…
We study the moduli space of four dimensional ordinary Lie algebras, and their versal deformations. Their classification is well known; our focus in this paper is on the deformations, which yield a picture of how the moduli space is…
In this paper, we introduce the notions of hom-Lie 2-algebras, which is the categorification of hom-Lie algebras, $HL_\infty$-algebras, which is the hom-analogue of $L_\infty$-algebras, and crossed modules of hom-Lie algebras. We prove that…
Transformation of operator algebras under Hopf algebra twist is studied. It is shown that that adjoint module algebras are stable under the twist. Applications to vector fields on non-commutative space-time are considered.
A twisted ring is a ring endowed with a family of endomorphisms satisfying certain relations. One may then consider the notions of twisted module and twisted differential module. We study them and show that, under some general hypothesis,…