Poisson Structures on Trivial Extension Algebras

被引：0

作者：

Garcia-Beltran, D. ^{[1
]}

Ruiz-Pantaleon, J. C. ^{[2
]}

Vorobiev, Yu. ^{[2
]}

机构：

[1] Univ Sonora, Dept Matemat, CONACyT, Hermosillo, Sonora, Mexico

[2] Univ Sonora, Dept Matemat, Hermosillo, Sonora, Mexico

来源：

BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY | 2023年 / 54卷 / 04期

关键词：

Poisson algebra; Trivial extension algebra; Poisson module; Contravariant derivative; Poisson cohomology; Poisson submanifold; Lie algebroid;

D O I：

10.1007/s00574-023-00366-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We present a class of Poisson structures on trivial extension algebras which generalizes some known structures induced by Poisson modules. We show that there exists a one-to-one correspondence between such a class of Poisson structures and some data involving (not necessarily flat) contravariant derivatives, and then we give a formulation of this result in terms of Lie algebroids. Some properties of the first Poisson cohomology are presented. Examples coming from Poissonmodules and Poisson sub-manifolds are given.

引用

页数：45

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