{"docId":10455,"paperId":10455,"url":"https:\/\/cm.episciences.org\/10455","doi":"10.46298\/cm.10455","journalName":"Communications in Mathematics","issn":"1804-1388","eissn":"2336-1298","volume":[{"vid":631,"name":"Volume 30 (2022), Issue 3 (Special issue: in memory of Arkady Onishchik)"}],"section":[],"repositoryName":"arXiv","repositoryIdentifier":"2204.11036","repositoryVersion":2,"repositoryLink":"https:\/\/arxiv.org\/abs\/2204.11036v2","dateSubmitted":"2022-12-11 09:53:43","dateAccepted":"2022-12-11 11:20:40","datePublished":"2022-12-14 12:51:51","titles":["Action of vectorial Lie superalgebras on some split supermanifolds"],"authors":["Onishchik, Arkady"],"abstracts":["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,","Comment: 8pp"],"keywords":["Mathematical Physics","Mathematics - Representation Theory","Primary 17A70, 17B20, 17B70, Secondary 70F25"]}