Finite-Dimensional Simple Poisson Modules

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• 作者：David A. Jordan (1)
  
• 关键词：Poisson module ; Poisson algebra ; Poisson automorphisms ; Primary 17B63 ; Secondary 16D60 ; 16S80 ; 16W22
• 刊名：Algebras and Representation Theory
• 出版年：2010
• 出版时间：February 2010
• 年：2010
• 卷：13
• 期：1
• 页码：79-101
• 全文大小：546KB
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• 作者单位：David A. Jordan (1)
  
  1. Department of Pure Mathematics, University of Sheffield, Hicks Building, Sheffield, S3聽7RH, UK
  
• ISSN：1572-9079

文摘

We prove a result that can be applied to determine the finite-dimensional simple Poisson modules over a Poisson algebra and apply it to numerous examples. In the discussion of the examples, the emphasis is on the correspondence with the finite-dimensional simple modules over deformations and on the behaviour of finite-dimensional simple Poisson modules on the passage from a Poisson algebra to the Poisson subalgebra of invariants for the action of a finite group of Poisson automorphisms.