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.
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收藏
页数：45
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