30 citations · 88 across the 36 of their papers we have counts for
36 papers
-structures and cohomology theory of compatible -operators and compatible dendriform algebras
Apurba Das, Shuangjian Guo, Yufei Qin
The notion of -operator is a generalization of the Rota-Baxter operator in the presence of a bimodule over an associative algebra. A compatible -operator…
Cohomology theory of Rota-Baxter pre-Lie algebras of arbitrary weights
Shuangjian Guo, Yufei Qin, Kai Wang +1
This paper is devoted to studying deformation, cohomology theory of Rota-Baxter pre-Lie algebras of arbitrary weights. First we give the notion of a new representation of a Rota-Ba…
Deformations and cohomology theory of Rota-Baxter -Lie algebras of arbitrary weights
Shuangjian Guo, Yufei Qin, Kai Wang +1
A cohomology theory of weighted Rota-Baxter -Lie algebras is introduced. Formal deformations, abelian extensions, skeletal weighted Rota-Baxter -Lie 2-algebras and crossed mo…
On equivariant Lie-Yamaguti algebras and related structures
Shuangjian Guo, Bibhash Mondal, Ripan Saha
In this paper, we first discuss cohomology and a one-parameter formal deformation theory of Lie-Yamaguti algebras. Next, we study finite group actions on Lie-Yamaguti algebras and…
On 3-Lie algebras with a derivation
Shuangjian Guo, Ripan Saha
In this paper, we study 3-Lie algebras with derivations. We call the pair consisting of a 3-Lie algebra and a distinguished derivation by the 3-LieDer pair. We define a cohomology…
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…
Rota-Baxter operators and related structures on anti-flexible algebras
Shuangjian Guo, Ripan Saha
In this paper, we first construct a graded Lie algebra which characterizes Rota-Baxter operators on an anti-flexible algebra as Maurer-Cartan elements. Next, we study infinitesimal…
On -type (equivariant) cohomology of Hom-pre-Lie algebras
Shuangjian Guo, Ripan Saha
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 natu…
Twisted relative Rota-Baxter operators on Leibniz algebras and NS-Leibniz algebras
Apurba Das, Shuangjian Guo
In this paper, we introduce twisted relative Rota-Baxter operators on a Leibniz algebra as a generalization of twisted Poisson structures. We define the cohomology of a twisted rel…
Relative Rota-Baxter systems on Leibniz algebras
Apurba Das, Shuangjian Guo
In this paper, we introduce relative Rota-Baxter systems on Leibniz algebras and give some characterizations and new constructions. Then we construct a graded Lie algebra whose Mau…
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…
On split regular BiHom-Poisson superalgebras
Shuangjian Guo, Yuanyuan Ke
The paper introduces the class of split regular BiHom-Poisson superalgebras, which is a natural generalization of split regular Hom-Poisson algebras and split regular BiHom-Lie sup…
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…