论文标题
分级泊松代数和相关特性的曲折
Twists of graded Poisson algebras and related properties
论文作者
论文摘要
我们介绍了一个分级联想代数的分级转折的泊松版本，并证明每个分级的泊松结构都在连接的分级分级的多项式环$ a：= \ bbbk [x_1，\ ldots，x_n] $上是$ a $ a $ a $ a $ a $ a $ a $ a $ a a $ a $ namy，nam nam $ a $， $π$ has a decomposition $$π=π_{unim} +\frac{1}{\sum_{i=1}^n {\rm deg} x_i} E\wedge {\mathbf m}$$ where $E$ is the Euler derivation, $π_{unim}$ is the unimodular graded Poisson structure on $ a $对应于$π$，$ {\ mathbf m} $是$（a，π）$的模块化推导。该结果是在二次设置中对相同结果的概括。研究了分级扭曲的刚度，$ ph^1 $ - 限制性和$ h $ ozoneness。作为一种应用，我们计算出势不可减少但不一定具有孤立的奇异性时，计算了三个变量的多项式环上的二次泊松结构的泊松同子。
We introduce a Poisson version of the graded twist of a graded associative algebra and prove that every graded Poisson structure on a connected graded polynomial ring $A:=\Bbbk[x_1,\ldots,x_n]$ is a graded twist of a unimodular Poisson structure on $A$, namely, if $π$ is a graded Poisson structure on $A$, then $π$ has a decomposition $$π=π_{unim} +\frac{1}{\sum_{i=1}^n {\rm deg} x_i} E\wedge {\mathbf m}$$ where $E$ is the Euler derivation, $π_{unim}$ is the unimodular graded Poisson structure on $A$ corresponding to $π$, and ${\mathbf m}$ is the modular derivation of $(A,π)$. This result is a generalization of the same result in the quadratic setting. The rigidity of graded twisting, $PH^1$-minimality, and $H$-ozoneness are studied. As an application, we compute the Poisson cohomologies of the quadratic Poisson structures on the polynomial ring of three variables when the potential is irreducible, but not necessarily having isolated singularities.
