论文标题
泊松代数的溶解度
Solvability of Poisson algebras
论文作者
论文摘要
令$ p $为带有lie bracket $ \ {，\} $的泊松代数，特征$ p \ geq 0 $。在本文中，研究了$ p $的谎言结构。特别是，如果$ p $可以解决其谎言括号，那么我们证明了由所有元素$ \ {\ {\ {x_1，x_1，x_2 \}生成的$ p $的poisson poisson poisson poisson $ \ nathcal {j} $ $ p $ ，x_5 \ in p $是索引的关联nilpotent，其范围为$ p $的函数。我们使用此结果进一步证明，如果$ p $是可解决的，而$ p \ neq 2 $，则泊松理想$ \ {p，p \} p $为nil。
Let $P$ be a Poisson algebra with a Lie bracket $\{, \}$ over a field $\F$ of characteristic $p\geq 0$. In this paper, the Lie structure of $P$ is investigated. In particular, if $P$ is solvable with respect to its Lie bracket, then we prove that the Poisson ideal $\mathcal{J}$ of $P$ generated by all elements $\{\{\{x_1, x_2\}, \{x_3, x_4\}\}, x_5\}$ with $x_1,\ldots ,x_5 \in P$ is associative nilpotent of index bounded by a function of the derived length of $P$. We use this result to further prove that if $P$ is solvable and $p\neq 2$, then the Poisson ideal $\{P,P\}P$ is nil.
