{"title":"向量李超代数对某些分裂超流形的作用","authors":"A. Onishchik","doi":"10.46298/cm.10455","DOIUrl":null,"url":null,"abstract":"The \"curved\" super Grassmannian is the supervariety of subsupervarieties of\npurely odd dimension $k$ in a~supervariety of purely odd dimension $n$, unlike\nthe \"usual\" super Grassmannian which is the supervariety of linear\nsubsuperspacies of purely odd dimension $k$ in a~superspace of purely odd\ndimension $n$. The Lie superalgebras of all and Hamiltonian vector fields on\nthe superpoint are realized as Lie superalgebras of derivations of the\nstructure sheaves of certain \"curved\" super Grassmannians,","PeriodicalId":37836,"journal":{"name":"Communications in Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2022-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Action of vectorial Lie superalgebras on some split supermanifolds\",\"authors\":\"A. Onishchik\",\"doi\":\"10.46298/cm.10455\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The \\\"curved\\\" super Grassmannian is the supervariety of subsupervarieties of\\npurely odd dimension $k$ in a~supervariety of purely odd dimension $n$, unlike\\nthe \\\"usual\\\" super Grassmannian which is the supervariety of linear\\nsubsuperspacies of purely odd dimension $k$ in a~superspace of purely odd\\ndimension $n$. The Lie superalgebras of all and Hamiltonian vector fields on\\nthe superpoint are realized as Lie superalgebras of derivations of the\\nstructure sheaves of certain \\\"curved\\\" super Grassmannians,\",\"PeriodicalId\":37836,\"journal\":{\"name\":\"Communications in Mathematics\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-04-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications in Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.46298/cm.10455\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.46298/cm.10455","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
Action of vectorial Lie superalgebras on some split supermanifolds
The "curved" super Grassmannian is the supervariety of subsupervarieties of
purely odd dimension $k$ in a~supervariety of purely odd dimension $n$, unlike
the "usual" super Grassmannian which is the supervariety of linear
subsuperspacies of purely odd dimension $k$ in a~superspace of purely odd
dimension $n$. The Lie superalgebras of all and Hamiltonian vector fields on
the superpoint are realized as Lie superalgebras of derivations of the
structure sheaves of certain "curved" super Grassmannians,
期刊介绍:
Communications in Mathematics publishes research and survey papers in all areas of pure and applied mathematics. To be acceptable for publication, the paper must be significant, original and correct. High quality review papers of interest to a wide range of scientists in mathematics and its applications are equally welcome.