Twisted Poincar\'{e} duality between Poisson homology and Poisson cohomology
Twisted Poincar\'{e} duality between Poisson homology and Poisson cohomology
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DOI：
10.1016/j.jalgebra.2014.08.023
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发表时间：
2014-04
期刊：
影响因子：
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通讯作者：
J.Luo;S.-Q. Wang;Q.-S. Wu
中科院分区：
文献类型：
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作者：
J.Luo;S.-Q. Wang;Q.-S. Wu
证明了值在任意Poisson模中的多项式Poisson代数的Poisson同调与上同调之间的扭曲Poincaré对偶。对偶性是通过以规范的方式扭曲泊松模结构来实现的，这种规范的方式是由模导子构造的。在Poisson结构是幺模的情况下，扭曲Poincaré对偶退化为通常意义下的Poincaré对偶。主要结果推广了Launois和Richard [8]关于二次Poisson结构和Zhu [25]关于线性Poisson结构的工作.
A version of the twisted Poincaré duality is proved between the Poisson homology and cohomology of a polynomial Poisson algebra with values in an arbitrary Poisson module. The duality is achieved by twisting the Poisson module structure in a canonical way, which is constructed from the modular derivation. In the case that the Poisson structure is unimodular, the twisted Poincaré duality reduces to the Poincaré duality in usual sense. The main result generalizes the work of Launois and Richard [8] for the quadratic Poisson structures and Zhu [25] for the linear Poisson structures.