{"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}
引用次数: 0
Abstract
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.