Reduced Poisson actions

Liu, Zhangju; Yang, Qilin

doi:10.1007/bf02898236

Sci. China Ser. A-Math.

2000

DOI: 10.1007/bf02898236

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Reduced Poisson actions

Zhangju Liu

Qilin Yang

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DG Poisson algebra and its universal enveloping algebra

Lü¹,

Wang²,

Zhuang³

2016

Sci. China Math.

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In this paper, we introduce the notions of differential graded (DG) Poisson algebra and DG Poisson module. Let $A$ be any DG Poisson algebra. We construct the universal enveloping algebra of $A$ explicitly, which is denoted by $A^{ue}$. We show that $A^{ue}$ has a natural DG algebra structure and it satisfies certain universal property. As a consequence of the universal property, it is proved that the category of DG Poisson modules over $A$ is isomorphic to the category of DG modules over $A^{ue}$. Furthermore, we prove that the notion of universal enveloping algebra $A^{ue}$ is well-behaved under opposite algebra and tensor product of DG Poisson algebras. Practical examples of DG Poisson algebras are given throughout the paper including those arising from differential geometry and homological algebra.Comment: Accepted by Science China Mathematic

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DG Poisson algebra and its universal enveloping algebra

Lü¹,

Wang²,

Zhuang³

2016

Sci. China Math.

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show abstract

Reduced Riemannian Poisson manifolds and Riemannian Poisson-Lie groups

Aloui

Zaalani

2020

Differential Geometry and its Applications

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Reduced Poisson actions

Cited by 2 publications

References 7 publications

DG Poisson algebra and its universal enveloping algebra

DG Poisson algebra and its universal enveloping algebra

Reduced Riemannian Poisson manifolds and Riemannian Poisson-Lie groups

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