30 citations · 66 across the 23 of their papers we have counts for
23 papers
Hom-Yang-Baxter equations and Hom-Yang-Baxter systems
Shengxiang Wang, Xiaohui Zhang, Shuangjian Guo
In this paper, we mainly present some new solutions of the Hom-Yang-Baxter equation from Hom-algebras, Hom-coalgebras and Hom-Lie algebras, respectively. Also, we prove that these…
The Hom-Long dimodule category and nonlinear equations
Shengxiang Wang, Xiaohui Zhang, Shuangjian Guo
In this paper, we construct a kind of new braided monoidal category over two Hom-Hopf algerbas and and associate it with two nonlinear equations. We first introduce…
On split regular Hom-Leibniz-Rinehart algebras
Shuangjian Guo, Xiaohui Zhang, Shengxiang Wang
In this paper, we introduce the notion of the Hom-Leibniz-Rinehart algebra as an algebraic analogue of Hom-Leibniz algebroid, and prove that such an arbitrary split regular Hom-Lei…
On BiHom-analogue of generalized Lie algebras
Shuangjian Guo, Xiaohui Zhang, Shengxiang Wang
In this paper, we introduce the definition of generalized BiHom-Lie algebras and generalized BiHom-Lie admissible algebras in the category of left modules for an…
On 3-Hom-Lie-Rinehart algebras
Shuangjian Guo, Xiaohui Zhang, Shengxiang Wang
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…
Representations and deformations of Hom-Lie-Yamaguti superalgebras
Shuangjian Guo, Xiaohui Zhang, Shengxiang Wang
Let be a Hom-Lie-Yamaguti superalgebra. We first introduce the representation and cohomology theory of Hom-Lie-Yamaguti superalgebras. Furthermore, we introduce the notion…
On the structure of split regular Hom-Lie Rinehart algebras
Shengxiang Wang, Xiaohui Zhang, Shuangjian Guo
The aim of this paper is to study the structures of split regular Hom-Lie Rinehart algebras. Let be a split regular Hom-Lie Rinehart algebra. We first show that is of t…
On split regular BiHom-Leibniz superalgebras
Shuangjian Guo, Shengxiang Wang
The goal of this paper is to study the structure of split regular BiHom-Leiniz superalgebras, which is a natural generalization of split regular Hom-Leiniz algebras and split regul…
Derivations and deformations of -Jordan Lie supertriple systems
Shengxiang Wang, Xiaohui Zhang, Shuangjian Guo
Let be a -Jordan Lie supertriple system. We first introduce the notions of generalized derivations and representations of and present some properties. Also, we study the…
-dervations of Lie color algebras
Yizheng Li, Shuangjian Guo
The aim of this article is to discuss the -derivation algebras of Lie color algebras. It is proved that, if the base ring contains , is a perfect Lie color al…
Central invariants and enveloping algebras of braided Hom-Lie algebras
Shengxiang Wang, Xiaohui Zhang, Shuangjian Guo
Let be a monoidal Hom-Hopf algebra and the Hom-Yetter-Drinfeld category over . Then in this paper, we first introduce the definition of braid…
The constructions of 3-Hom-Lie bialgebras
Shuangjian Guo, Xiaohui Zhang, Shengxiang Wang
In this paper, we first introduce the notion of a 3-Hom-Lie bialgebra and prove that it is equivalent to a Manin triple of 3-Hom-Lie algebras. Also, we study the -oper…
Some results on -Hom-Jordan Lie conformal superalgebras
Shuangjian Guo, Shengxiang Wang
In this paper, we introduce the representation theory of -Hom-Jordan Lie conformal superalgebras and discuss the cases of adjoint representations. Furthermore, we develop the co…
Cohomology and derivations of BiHom-Lie conformal algebras
Shuangjian Guo, Xiaohui Zhang, Shengxiang Wang
In this paper, we introduce the notion of a BiHom-Lie conformal algebra and develop its cohomology theory. Also, we discuss some applications to the study of deformations of regula…
The construction of Hom left-symmetric conformal bialgebras
Shuangjian Guo, Xiaohui Zhang, Shengxiang Wang
In this paper, we first introduce the notion of Hom-left-symmetric conformal bialgebras and show some nontrivial examples. Also, we present construction methods of matched pairs of…
Manin triples and quasitriangular structures of Hom-Poisson bialgebras
Shuangjian Guo, Xiaohui Zhang, Shengxiang Wang
In this paper, we first introduce the definition of a Hom-Poisson bialgebra and give an equivalent descriptions via the Manin triple of Hom-Poisson algebras. Also we introduce noti…
Representations and derivations of Hom-Lie conformal superalgebras
Shuangjian Guo, Lihong Dong, Shengxiang Wang
In this paper, we introduce a representation theory of Hom-Lie conformal superalgebras and discuss the cases of adjoint representations. Furthermore, we develop cohomology theory o…
The construction and deformation of BiHom-Novikov agebras
Shuangjian Guo, Xiaohui Zhang, Shengxiang Wang
BiHom-Novikov agebra is a generalized Hom-Novikov algebra endowed with two commuting multiplicative linear maps. The main purpose of this paper is to show that two classes of BiHom…
BiHom-Lie superalgebra structures
Shengxiang Wang, Shuangjian Guo
The aim of this paper is to introduce the notion of BiHom-Lie superalgebras. This class of algebras is a generalization of both BiHom-Lie algebras and Hom-Lie superalgebras. In thi…
Yetter-Drinfeld modules for weak Hom-Hopf algebras
Shuangjian Guo, Yizheng Li, Shengxiang Wang
The aim of this paper is to define and study Yetter-Drinfeld modules over weak Hom-Hopf algebras. We show that the category of Yetter-Drinfeld modules with bijec…
Enveloping actions for twisted partial actions
Shuangjian Guo, Shengxiang Wang
Let A#_{α, ω}H be a partial crossed product. In this paper, we first generalize the theorem about the existence of an enveloping action to twisted partial actions. Second, we const…
Relative Hom-Hopf modules and total integrals
Shuangjian Guo, Xiaohui Zhang, Shengxiang Wang
Let $(H, \a)$ be a monoidal Hom-Hopf algebra and $(A, \b)$ a right $(H, \a)$-Hom-comodule algebra. We first investigate the criterion for the existence of a total integral of $(A,…
Braided monoidal categories and Doi Hopf modules for monoidal Hom-Hopf algebras
Shuangjian Guo, Xiaohui Zhang, Shengxiang Wang
We first introduce the notion of Doi Hom-Hopf modules and find the sufficient condition for the category of Doi Hom-Hopf modules to be monoidal. Also we obtain the condition for th…