{"title":"Foundations of Lie theory for -structures and some of its applications","authors":"V. Gorbatsevich","doi":"10.1070/IM9115","DOIUrl":null,"url":null,"abstract":"We construct an analogue of classical Lie theory in the case of Lie groups and Lie algebras defined over the algebra of dual numbers. As an application, we study approximate symmetries of differential equations and construct analogues of Hjelmslev’s natural geometry.","PeriodicalId":54910,"journal":{"name":"Izvestiya Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Izvestiya Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1070/IM9115","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We construct an analogue of classical Lie theory in the case of Lie groups and Lie algebras defined over the algebra of dual numbers. As an application, we study approximate symmetries of differential equations and construct analogues of Hjelmslev’s natural geometry.
期刊介绍：
The Russian original is rigorously refereed in Russia and the translations are carefully scrutinised and edited by the London Mathematical Society. This publication covers all fields of mathematics, but special attention is given to:
Algebra;
Mathematical logic;
Number theory;
Mathematical analysis;
Geometry;
Topology;
Differential equations.
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