{"title":"二重(拟)泊松代数的态射与可积系统的作用角对偶","authors":"M. Fairon","doi":"10.5802/ahl.121","DOIUrl":null,"url":null,"abstract":"Double (quasi-)Poisson algebras were introduced by Van den Bergh as non-commutative analogues of algebras endowed with a (quasi-)Poisson bracket. In this work, we provide a study of morphisms of double (quasi-)Poisson algebras, which we relate to the $H_0$-Poisson structures of Crawley-Boevey. We derive from our results a representation theoretic description of action-angle duality for several classical integrable systems.","PeriodicalId":192307,"journal":{"name":"Annales Henri Lebesgue","volume":"38 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"Morphisms of double (quasi-)Poisson algebras and action-angle duality of integrable systems\",\"authors\":\"M. Fairon\",\"doi\":\"10.5802/ahl.121\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Double (quasi-)Poisson algebras were introduced by Van den Bergh as non-commutative analogues of algebras endowed with a (quasi-)Poisson bracket. In this work, we provide a study of morphisms of double (quasi-)Poisson algebras, which we relate to the $H_0$-Poisson structures of Crawley-Boevey. We derive from our results a representation theoretic description of action-angle duality for several classical integrable systems.\",\"PeriodicalId\":192307,\"journal\":{\"name\":\"Annales Henri Lebesgue\",\"volume\":\"38 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-08-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annales Henri Lebesgue\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5802/ahl.121\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales Henri Lebesgue","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5802/ahl.121","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 4
摘要
重(拟)泊松代数是Van den Bergh引入的具有(拟)泊松括号的代数的非交换类似物。在这项工作中，我们研究了双(拟)泊松代数的态射，这与Crawley-Boevey的$H_0$-泊松结构有关。从这些结果中，我们得到了几个经典可积系统的作用角对偶的表示理论描述。
Morphisms of double (quasi-)Poisson algebras and action-angle duality of integrable systems
Double (quasi-)Poisson algebras were introduced by Van den Bergh as non-commutative analogues of algebras endowed with a (quasi-)Poisson bracket. In this work, we provide a study of morphisms of double (quasi-)Poisson algebras, which we relate to the $H_0$-Poisson structures of Crawley-Boevey. We derive from our results a representation theoretic description of action-angle duality for several classical integrable systems.
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