{"title":"阿贝尔纳什流形的分类","authors":"Yixin Bao, Yangyang Chen","doi":"10.1090/proc/15743","DOIUrl":null,"url":null,"abstract":"By the algebraization of affine Nash groups, a connected affine Nash group is an abelian Nash manifold if and only if its algebraization is a real abelian variety. We first classify real abelian varieties up to isomorphisms. Then with a bit more efforts, we classify abelian Nash manifolds up to Nash equivalences.","PeriodicalId":275006,"journal":{"name":"arXiv: Representation Theory","volume":"40 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Classification of abelian Nash manifolds\",\"authors\":\"Yixin Bao, Yangyang Chen\",\"doi\":\"10.1090/proc/15743\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"By the algebraization of affine Nash groups, a connected affine Nash group is an abelian Nash manifold if and only if its algebraization is a real abelian variety. We first classify real abelian varieties up to isomorphisms. Then with a bit more efforts, we classify abelian Nash manifolds up to Nash equivalences.\",\"PeriodicalId\":275006,\"journal\":{\"name\":\"arXiv: Representation Theory\",\"volume\":\"40 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-10-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Representation Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1090/proc/15743\",\"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: Representation Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/proc/15743","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
By the algebraization of affine Nash groups, a connected affine Nash group is an abelian Nash manifold if and only if its algebraization is a real abelian variety. We first classify real abelian varieties up to isomorphisms. Then with a bit more efforts, we classify abelian Nash manifolds up to Nash equivalences.
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