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Action of vectorial Lie superalgebras on some split supermanifolds

Mathematical Physics 2023-06-22 v2 math.MP Representation Theory

Abstract

The "curved" super Grassmannian is the supervariety of subsupervarieties of purely odd dimension kk in a~supervariety of purely odd dimension nn, unlike the "usual" super Grassmannian which is the supervariety of linear subsuperspacies of purely odd dimension kk in a~superspace of purely odd dimension nn. 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,

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Cite

@article{arxiv.2204.11036,
  title  = {Action of vectorial Lie superalgebras on some split supermanifolds},
  author = {Arkady Onishchik},
  journal= {arXiv preprint arXiv:2204.11036},
  year   = {2023}
}

Comments

8pp