11 citations · 24 across the 17 of their papers we have counts for
13 papers · 1 filter
Geometry and classifications of some -Lie algebras
Yin Chen, Shan Ren, Runxuan Zhang
Using group actions and orbit-stabilizer methods, we study the geometry of isomorphism classes of finite-dimensional -Lie algebras over a field of characteristic $\…
Generalized derivations of -Lie algebras
Yin Chen, Shan Ren, Jiawen Shan +1
This article explores the structure theory of compatible generalized derivations of finite-dimensional -Lie algebras over a field . We prove that any compatible quas…
Deformations of left-symmetric color algebras
Yin Chen, Runxuan Zhang
We develop a deformation theory for finite-dimensional left-symmetric color algebras, which can be used to construct new algebraic structures and interpret left-symmetric color coh…
Cohomology of left-symmetric color algebras
Yin Chen, Runxuan Zhang
We develop a new cohomology theory for finite-dimensional left-symmetric color algebras and their finite-dimensional bimodules, establishing a connection between Lie color cohomolo…
Kupershmidt-Nijenhuis structures on pre-Malcev algebras
Yin Chen, Liman Qin, Shan Ren +1
We study Kupershmidt operators, Nijenhuis operators, and Kupershmidt-Nijenhuis structures on finite-dimensional pre-Malcev algebras over a field of characteristic zero. We construc…
Poisson Yang-Baxter equations and -operators of Poisson superalgebras
Jiawen Shan, Runxuan Zhang
We investigate connections between -operators of Poisson superalgebras and skew-symmetric solutions of the Poisson Yang-Baxter equation (PYBE). We prove that a skew-s…
A generalization on derivations of Lie algebras
Hongliang Chang, Yin Chen, Runxuan Zhang
We initiate a study on a range of new generalized derivations of finite-dimensional Lie algebras over an algebraically closed field of characteristic zero. This new generalization…
Representations of -Lie Algebras and Tailed Derivations of Lie Algebras
Runxuan Zhang
We study the representation theory of finite-dimensional -Lie algebras over the complex field. We derive an -Lie version of the classical Lie's theorem, i.e., any finite-dime…
A commutative algebra approach to multiplicative Hom-Lie algebras
Yin Chen, Runxuan Zhang
Let be a finite-dimensional complex Lie algebra and be the affine variety of all multiplicative Hom-Lie algebras on .…
Derivations, Automorphisms, and Representations of Complex -Lie Algebras
Yin Chen, Ziping Zhang, Runxuan Zhang +1
Let be a finite-dimensional non-Lie complex -Lie algebra. We study the derivation algebra and the automorphism group o…
Classification of three dimensional complex omega-Lie algebras
Yin Chen, Chang Liu, Run-Xuan Zhang
A complex -Lie algebra is a vector space over the complex field, equipped with a skew symmetric bracket and a bilinear form such that $$[[x,y],z]+[[y,z],x]+ [[z,…
Cohomologies and Deformations of Generalized Left-symmetric Algebras
Run-Xuan Zhang
The purpose of this paper is to develop a cohomology and deformation theories for generalized left-symmetric algebras.We introduce the notions of generalized left-symmetric cohomol…
Left-symmetric Structures on Complex Simple Lie Superalgebras
Run-Xuan Zhang
A well-known fact is that there does not exist any compatible left-symmetric structures on a finite-dimensional complex semisimple Lie algebra (see \cite{Chu1974}). This result is…