10.46298/cm.10456
https://cm.episciences.org/10456
Onishchik, Arkady
Arkady
Onishchik
Transitive irreducible Lie superalgebras of vector fields
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
episciences.org
Mathematics - Representation Theory
32C11, 17B20
Attribution 4.0 International (CC BY 4.0)
2022-12-11
2022-12-14
2022-12-14
eng
journal article
arXiv:2204.11033
10.48550/arXiv.2204.11033
2336-1298
https://cm.episciences.org/10456/pdf
VoR
application/pdf
Communications in Mathematics
Volume 30 (2022), Issue 3 (Special issue: in memory of Arkady Onishchik)
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