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Communications in Mathematics
23361298
12
14
2022
Volume 30 (2022), Issue 3...
Transitive irreducible Lie superalgebras of vector fields
Arkady
Onishchik
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 finitedimensional 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 $0n$dimensional supervariety.
12
14
2022
10456
https://creativecommons.org/licenses/by/4.0
arXiv:2204.11033
10.48550/arXiv.2204.11033
10.46298/cm.10456
https://cm.episciences.org/10456

https://cm.episciences.org/10456/pdf

https://cm.episciences.org/10456/pdf