Vector fields on $\Pi$-symmetric flag supermanifolds

Abstract

The main result of this paper is the computation of the Lie superalgebras of holomorphic vector fields on the complex $\Pi$-symmetric flag supermanifolds, introduced by Yu.I.~Manin. We prove that with one exception any vector field is fundamental with respect to the natural action of the Lie superalgebra ${\mathfrak{q}}_n(\mathbb{C})$.

Cited by in corpus (1)

• Non-split supermanifolds associated with the cotangent bundle