{"docId":10456,"paperId":10456,"url":"https:\/\/cm.episciences.org\/10456","doi":"10.46298\/cm.10456","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":"2204.11033","repositoryVersion":2,"repositoryLink":"https:\/\/arxiv.org\/abs\/2204.11033v2","dateSubmitted":"2022-12-11 10:02:56","dateAccepted":"2022-12-11 11:21:46","datePublished":"2022-12-14 12:51:42","titles":["Transitive irreducible Lie superalgebras of vector fields"],"authors":["Onishchik, Arkady"],"abstracts":["Let $\\mathfrak{d}$ be the Lie superalgebra of superderivations of the sheaf of sections of the exterior algebra of the homogeneous vector bundle $E$ over the flag variety $G\/P$, where $G$ is a simple finite-dimensional complex Lie group and $P$ its parabolic subgroup. Then, $\\mathfrak{d}$ is transitive and irreducible whenever $E$ is defined by an irreducible $P$-module $V$ such that the highest weight of $V^*$ is dominant. Moreover, $\\mathfrak{d}$ is simple; it is isomorphic to the Lie superalgebra of vector fields on the superpoint, i.e., on a $0|n$-dimensional supervariety.","Comment: 16 pages"],"keywords":["Mathematics - Representation Theory","32C11, 17B20"]}