7 papers
Classification of Novikov-Poisson Algebras and Their Applications
Ziyi Zhang, Zeyu Hao, Yining Sun +1
In this paper, we give a complete classification, up to isomorphism, of 3-dimensional complex Novikov--Poisson algebras. As an application of the classification, we further prove t…
Gelfand--Dorfman Algebras: Nilpotency, Solvability, Construction and Classification
Ziyi Zhang, Zeyu Hao, Yining Sun +1
In this paper, we characterize the nilpotency and solvability of Gelfand--Dorfman (GD) algebras. In contrast with Poisson algebras and transposed Poisson algebras, we give examples…
-Generalized Hessian pre-Lie algebras and -Generalized Yang--Baxter Equations
Yining Sun, Zeyu Hao, Ziyi Zhang +1
Inspired by the problem of constructing (-)pre-Lie algebra structures on the dual space of a pre-Lie algebra, we introduce the \(A\)-generalized Yang--Baxter equation as a gener…
-Lie bialgebras and -Yang-Baxter equation
Yining Sun, Zeyu Hao, Ziyi Zhang +1
In this paper, we introduce the definition of multiplicative -Lie bialgebra, which is equivalent to the Manin triples and matched pairs. We also study the -Yang-Baxter equati…
Cohomology of a restricted Lie algebra with a restricted derivation in characteristic 2
Dan Mao, Liangyun Chen
This paper mainly studies the ResLieDer pair in characteristic 2, that is, a restricted Lie algebra with a restricted derivation. We define the restricted representation of a ResLi…
Double Extensions of Multiplicative Restricted Hom-Lie Algebras
Dan Mao, Zeyu Hao, Liangyun Chen
In this paper, we study the double extension of a restricted quadratic Hom-Lie algebra , which is an enlargement of by means of a central ext…
Modular structure theory on Hom-Lie algebras
Dan Mao, Baoling Guan, Liangyun Chen
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 thi…