Vector fields on \(\mathfrak{gl}_{m|n}(\mathbb{C})\)-flag supermanifolds. (English) Zbl 1355.17025
Summary: The main result of this paper is the computation of the Lie superalgebras of holomorphic vector fields on complex flag supermanifolds, introduced by Yu.I. Manin. We prove that with several exceptions any holomorphic vector field is fundamental with respect to the natural action of the Lie superalgebra \(\mathfrak{gl}_{m|n}(\mathbb{C})\).
MSC:
| 17B66 | Lie algebras of vector fields and related (super) algebras |
| 32C11 | Complex supergeometry |
| 58A50 | Supermanifolds and graded manifolds |
References:
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