5 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…
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…