无限维李代数对称代数的泊松基定理

IF 0.8 4区数学 Q2 MATHEMATICS

Arkiv for Matematik Pub Date : 2023-01-01 DOI:10.4310/arkiv.2023.v61.n2.a6

Omar Leon Sanchez, Susan J. Sierra

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引用次数: 3

摘要

考虑具有自然泊松括号的无限维李代数的对称代数满足泊松理想上的升链条件(ACC)。我们在一个分级李代数上定义了一个组合条件，我们称之为Dicksonian，因为它与Dickson关于$\mathbb N^k$的有限子集的引理有关。我们的主要结果是:

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A Poisson basis theorem for symmetric algebras of infinite-dimensional Lie algebras

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:

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来源期刊

Arkiv for Matematik 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publishing research papers, of short to moderate length, in all fields of mathematics.