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math.RA2026
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…
math.RA2026
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…
math.RA2025
-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…