Two families of flag supermanifolds
type: Item
instance of: scholarly article
title: Two families of flag supermanifolds
zbMATH Open document ID: 0814.58003
DOI: 10.1016/0926-2245(94)90003-5
author: V. A. Bunegina
author: A. L. Onishchik
published in: Differential Geometry and its Applications
publication date: 1994-01-01T00:00:00Z
review text: The authors construct two one-parametric analytic families of compact complex supermanifolds admitting a transitive action of the family of exceptional Lie superalgebras \(D(2,1;\alpha)\). The isotropy subalgebras of these actions are parabolic. The first family contains the projective superline \(\mathbb{C} \mathbb{P}^{1| 4}\), and the second one the super- Grassmannian \(G_{2| 2, 1| 1}\). The tangent sheaf cohomology of the constructed supermanifolds is computed.
Mathematics Subject Classification ID: 58A50
Mathematics Subject Classification ID: 17C70
zbMATH DE Number: 729272
zbMATH Keywords: flag manifold
zbMATH Keywords: deformation
zbMATH Keywords: Lie superalgebra
zbMATH Keywords: super-Grassmannian
zbMATH Keywords: supermanifolds
Wikidata QID: Q115362613
MaRDI profile type: Publication
full work available at URL: 0926-2245(94)90003-5
OpenAlex ID: W2083161686
cites work: Q4096161
cites work: Homogeneous vector bundles
cites work: Q4309599
cites work: Lie superalgebras
cites work: Q4130629
cites work: Q3998175
cites work: Q3816325
cites work: Q4010538
cites work: The theory of Lie superalgebras. An introduction
cites work: Irreducible representations of the exceptional Lie superalgebras D(2,1;α)
cites work: Analytic Geometry of Complex Superspaces
cites work: On the rigidity of super-Grassmannians
description: scientific article; zbMATH DE number 729272