eng
episciences.org
Communications in Mathematics
1804-1388
2336-1298
2022-12-14
Volume 30 (2022), Issue 3...
10.46298/cm.10456
10456
journal article
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 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.
https://cm.episciences.org/10456/pdf
Mathematics - Representation Theory
32C11, 17B20