{"title":"诺维科夫共形代数的微分包络","authors":"P. S. Kolesnikov, A. A. Nesterenko","doi":"arxiv-2409.10029","DOIUrl":null,"url":null,"abstract":"A Novikov conformal algebra is a conformal algebra such that its coefficient\nalgebra is right-symmetric and left commutative (i.e., it is an ``ordinary''\nNovikov algebra). We prove that every Novikov conformal algebra with a\nuniformly bounded locality function on a set of generators can be embedded into\na commutative conformal algebra with a derivation. In particular, every\nfinitely generated Novikov conformal algebra has a commutative conformal\ndifferential envelope. For infinitely generated algebras this statement is not\ntrue in general.","PeriodicalId":501136,"journal":{"name":"arXiv - MATH - Rings and Algebras","volume":"196 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Differential envelopes of Novikov conformal algebras\",\"authors\":\"P. S. Kolesnikov, A. A. Nesterenko\",\"doi\":\"arxiv-2409.10029\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A Novikov conformal algebra is a conformal algebra such that its coefficient\\nalgebra is right-symmetric and left commutative (i.e., it is an ``ordinary''\\nNovikov algebra). We prove that every Novikov conformal algebra with a\\nuniformly bounded locality function on a set of generators can be embedded into\\na commutative conformal algebra with a derivation. In particular, every\\nfinitely generated Novikov conformal algebra has a commutative conformal\\ndifferential envelope. For infinitely generated algebras this statement is not\\ntrue in general.\",\"PeriodicalId\":501136,\"journal\":{\"name\":\"arXiv - MATH - Rings and Algebras\",\"volume\":\"196 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Rings and Algebras\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.10029\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Rings and Algebras","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.10029","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Differential envelopes of Novikov conformal algebras
A Novikov conformal algebra is a conformal algebra such that its coefficient
algebra is right-symmetric and left commutative (i.e., it is an ``ordinary''
Novikov algebra). We prove that every Novikov conformal algebra with a
uniformly bounded locality function on a set of generators can be embedded into
a commutative conformal algebra with a derivation. In particular, every
finitely generated Novikov conformal algebra has a commutative conformal
differential envelope. For infinitely generated algebras this statement is not
true in general.