{"title":"A Poisson basis theorem for symmetric algebras of infinite-dimensional Lie algebras","authors":"Omar Leon Sanchez, Susan J. Sierra","doi":"10.4310/arkiv.2023.v61.n2.a6","DOIUrl":null,"url":null,"abstract":"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: ","PeriodicalId":55569,"journal":{"name":"Arkiv for Matematik","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Arkiv for Matematik","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4310/arkiv.2023.v61.n2.a6","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 3
Abstract
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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