7 papers
The geometric classification of Novikov-Poisson and Gelfand-Dorfman algebras
Zeyu Hao, Ivan Kaygorodov, Azamat Saydaliyev +1
We give the geometric classification of complex 3-dimensional Novikov-Poisson and Gelfand-Dorfman algebras. In particular, we prove that the variety of complex 3-dimensional Noviko…
Local derivations is a Lie algebra
Zeyu Hao, Liangyun Chen
In this paper, we utilize the reflexive hull to unify the concepts of local and almost inner derivations. By investigating the algebraic structure of reflexive hulls, we prove the…
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…
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…