21 citations · 177 across the 58 of their papers we have counts for
61 papers
Derived equivalences and delooping levels
Liang Chen
We construct a finite-dimensional algebra derived equivalent to the example of Kershaw--Rickard. For the Kershaw--Rickard example the delooping level and the sub-derived delooping…
Cohomologies of pre-LieDer pairs and applications
Shanshan Liu, Liangyun Chen
In this paper, we use the higher derived bracket to give the controlling algebra of pre-LieDer pairs. We give the cohomology of pre-LieDer pairs by using the twist -algeb…
Deformations and abelian extensions of compatible pre-Lie algebras
Shanshan Liu, Liangyun Chen
In this paper, we first give the notation of a compatible pre-Lie algebra and its representation. We study the relation between compatible Lie algebras and compatible pre-Lie algeb…
Deformations and abelian extensions on anti-pre-Lie algebras
Shanshan Liu, Zhao Chen, Liangyun Chen
In this paper, we introduce the representation of anti-pre-Lie algebras and give the second cohomology group of anti-pre-Lie algebras. As applications, first, we study linear defor…
Deformations of relative Rota-Baxter operators on Leibniz Triple Systems
Xueru Wu, Yao Ma, Liangyun Chen
In this paper, we introduce the cohomology theory of relative Rota-Baxter operators on Leibniz triple systems. We use the cohomological approach to study linear and formal deformat…
Relative Rota-Baxter operators of nonzero weights on Lie Triple Systems
Xueru Wu, Yao Ma, Liangyun Chen
In this paper, we introduce the notion of a relative Rota-Baxter operator of weight on a Lie triple system with respect to an action on another Lie triple system, which can be…
Classification of simple Harish-Chandra modules over the Ovsienko-Roger superalgebra
Munayim Dilxat, Liangyun Chen, Dong Liu
With the -operators for the Virasoro algebra \cite{BF} and the super Virasoro algebra in \cite{CL, CLL}, we get the -operators for the Ovsienko-Roger superalgebras in this pa…
Biderivations, commuting mappings and (2-)local derivations of -graded Lie algebras of maximal class
Yong Yang, Liming Tang, Liangyun Chen
In Fialowski's classification for algebras of maximal class, there are three Lie algebras of maximal class with 1-dimensional homogeneous components: , and $\…
Cohomologies and crossed modules for pre-Lie Rinehart algebras
Liangyun Chen, Meijun Liu, Jiefeng Liu
A pre-Lie-Rinehart algebra is an algebraic generalization of the notion of a left-symmetric algebroid. We construct pre-Lie-Rinehart algebras from r-matrices through Lie algebra ac…
Cohomology of Leibniz Triple Systems and its applications
Xueru Wu, Liangyun Chen, Yao Ma
In this paper, we introduce the first and third cohomology groups on Leibniz triple systems, which can be applied to extension theory and -parameter formal deformation theory. S…
Conformal $(\si,\t)$-Derivations on Lie conformal superalgebras
Tianqi Feng, Jun Zhao, Liangyun Chen
In this paper, we focus on the $(\si,\t)$-derivation theory of Lie conformal superalgebras. Firstly, we study the fundamental properties of conformal $(\si,\t)$-derivations. Second…
Rota-Baxter operators on Turaev's Hopf group (co)algebras I: Basic definitions and related algebraic structures
Tianshui Ma, Jie Li, Liangyun Chen +1
We find a natural compatible condition between the Rota-Baxter operator and Turaev's (Hopf) group-(co)algebras, which leads to the concept of Rota-Baxter Turaev's (Hopf) group-(co)…
Product and complex structures on 3-Bihom-Lie algebras
Juan Li, Ying Hou, Liangyun Chen
In this paper, we first introduce the notion of a product structure on a -Bihom-Lie algebra which is a Nijenhuis operator with some conditions. And we provide that a -Bihom-L…
Algebras of quotients and Martindale-like quotients of Leibniz algebras
Chenrui Yao, Yao Ma, Liming Tang +1
In this paper, the definitions of algebras of quotients and Martandale-like qoutients of Leibniz algebras are introduced and the interactions between the two quotients are determin…
Super-Biderivations and Linear Super-Commuting Maps on the Lie Superalgebras
Liming Tang, Lingyi Meng, Liangyun Chen
Suppose the ground field is algebraically closed and of characteristic different from 2. In this paper, we described the intrinsic connections among linear super-commuting maps, su…
Algebras of quotients of Hom-Lie algebras
Chenrui Yao, Liangyun Chen
In this paper, we introduce the notion of algebras of quotients of Hom-Lie algebras and investigate some properties which can be lifted from a Hom-Lie algebra to its algebra of quo…
Biderivations and commuting linear maps on Hom-Lie algebras
Bing Sun, Yao Ma, Liangyun Chen
The purpose of this paper is to determine skew-symmetric biderivations and commuting linear maps on a Hom-Lie algebra hav…
On Hom-Groups and Hom-Group actions
Liangyun Chen, Tianqi Feng, Yao Ma +2
A Hom-group is the non-associative generalization of a group, whose associativity and unitality are twisted by a compatible bijective map. In this paper, we give some new examples…
Generalized derivations, quasiderivations and centroids of ternary Jordan algebras
Chenrui Yao, Yao Ma, Liangyun Chen
In this paper, we give some construction about ternary Jordan algebras at first. Next we study relationships between generalized derivations, quasiderivations and centroids of tern…
The construction of 3-Bihom-Lie algebras
Juan Li, Liangyun Chen
The purpose of this paper is to study the construction of -Bihom-Lie algebras. We give some ways of constructing -Bihom-Lie algebras from -Bihom-Lie algebras and -total…
Structure of multiplicative simple Hom-Jordan algebras
Chenrui Yao, Yao Ma, Liangyun Chen
In this paper, we mainly study structure of multiplicative simple Hom-Jordan algebras. We talk about equivalent conditions for multiplicative Hom-Jordan algebras being solvable, si…
Super-biderivations of the contact Lie superalgebra
Xiaodong Zhao, Yuan Chang, Xin Zhou +1
Let denote the contact Lie superalgebra over a field of characteristic , which has a finite -graded structure. Let be the canonica…
Derivations on semi-simple Jordan algebras and its applications
Chenrui Yao, Yao Ma, Liangyun Chen
In this paper, we mainly study the derivation algebras of semi-simple Jordan algebras over a field of characteristic and give sufficient and necessary conditions that the deriv…
Generalized derivations of Hom-Jordan algebras
Chenrui Yao, Yao Ma, Liangyun Chen
In this paper, we give some properties of generalized derivation algebras of Hom-Jordan algebras. In particular, we show that , the sum of the quasideriv…