Poisson Structures on Trivial Extension Algebras

2021/09/08 by D. García-Beltrán, García-Beltrán, D., J. C. Ruíz-Pantaleón +3
Mathematics · #16W25 #17B60 #17B63 #53D17 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA) #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2109.03460

openalex publication_date 2021/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We present a class of Poisson structures on trivial extension algebras which generalize 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 also presented. Examples coming from Poisson modules and Poisson submanifolds are given.

Related

• Poisson structures on associated with rigid Lie algebras
• Poincare Duality For Smooth Poisson Algebras And BV Structure On Poisson Cohomology
• Poisson structures of divisor-type
• Noncommutative Poisson structures, derived representation schemes and Calabi-Yau algebras
• Finite-dimensional simple Poisson modules