论文标题
无限二维谎言代数对称代数的泊松定理
A Poisson basis theorem for symmetric algebras of infinite-dimensional Lie algebras
论文作者
论文摘要
我们考虑何时配备有天然泊松支架的无限尺寸谎言代数的对称代数满足泊松理想的上升链条件（ACC）。我们在分级的谎言代数上定义了组合条件，我们称之为迪克森尼人，因为它与迪克森在$ \ mathbb n^k $的有限亚集的诱饵有关。我们的主要结果是： 定理。如果$ \ mathfrak g $是迪克森分级的谎言代数，那么在一个特征性零的领域，那么对称代数$ s（\ mathfrak g）$ $ s可以满足激进的泊松理想的ACC。 作为一种应用，我们为在特征零的代数闭合场以及virasoro代数的对称代数上建立了多项式生长的任何分级简单代数的对称代数的ACC。我们还引发了与有限泊松生成的代数的泊松原始光谱有关的一些后果。
We consider when the symmetric algebra of an infinite-dimensional Lie algebra, equipped with the natural Poisson bracket, satisfies the ascending chain condition (ACC) on Poisson ideals. We define a combinatorial condition on a graded Lie algebra which we call Dicksonian because it is related to Dickson's lemma on finite subsets of $\mathbb N^k$. Our main result is: Theorem. If $\mathfrak g$ is a Dicksonian graded Lie algebra over a field of characteristic zero, then the symmetric algebra $S(\mathfrak g)$ satisfies the ACC on radical Poisson ideals. As an application, we establish this ACC for the symmetric algebra of any graded simple Lie algebra of polynomial growth over an algebraically closed field of characteristic zero, and for the symmetric algebra of the Virasoro algebra. We also derive some consequences connected to the Poisson primitive spectrum of finitely Poisson-generated algebras.
