泊松代数模的无穷小形变
Infinitesimal Deformation of the Module of Poisson Algebras
DOI: 10.12677/AAM.2021.105151, PDF,   
作者: 赵 宁：辽宁师范大学数学学院，辽宁 大连
关键词: 泊松代数；Nijenhuis算子；无穷小形变；Poisson Algebra； Nijenhuis Operator； Infinitesimal Deformation
摘要: 本文主要研究泊松代数模的无穷小形变。构造了泊松代数的形变，以及泊松代数模的无穷小形变，讨论两个无穷小形变的等价条件和模的无穷小形变是平凡的条件。文章的最后给出了泊松代数上Nijenhuis算子的定义，并且找到泊松代数模的平凡形变与Nijenhuis算子结构的关系。
Abstract: In this paper, we study the infinitesimal deformation of the module of Poisson algebra. The deformation of Poisson algebra is constructed, the infinitesimal deformation of the module of Poisson algebra and the equivalent condition of two infinitesimal deformations are discussed. At the end of the paper, the Nijenhuis operators of Poisson algebras are given, and the relationship between trivial deformation and Nijenhuis operator structure is also found.
文章引用：赵宁. 泊松代数模的无穷小形变[J]. 应用数学进展, 2021, 10(5): 1418-1427. https://doi.org/10.12677/AAM.2021.105151

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