Geodesic
The Splitting Problem for Complex Homogeneous Supermanifolds
Elizaveta Vishnyakova1
1Université du Luxembourg, 6 rue Richard Coudenhove-Kalergi, 1359 Luxembourg
Journal of Lie Theory, Tome 25 (2015) no. 2, pp. 459-476

Voir la notice de l'article provenant de la source Heldermann Verlag

It is a classical result that any complex analytic Lie supergroup G is split (see J.-L. Koszul, Graded manifolds and graded Lie algebras, Proceeding of the International Meeting on Geometry and Physics (Bologna), Pitagora, 71--84 (1982)), that is, its structure sheaf is isomorphic to the structure sheaf of a certain vector bundle. However, there do exist non-split complex analytic homogeneous supermanifolds.
We study the question how to find out whether a complex analytic homogeneous supermanifold is split or non-split. Our main result is a description of left invariant gradings on a complex analytic homogeneous supermanifold G/H in the terms of H-invariants. As a corollary to our investigations we get some simple sufficient conditions for a complex analytic homogeneous supermanifold to be split in terms of Lie algebras.
Classification : 51P05, 53Z05, 32M10
Mots-clés : Lie supergroup, complex homogeneous supermanifold

Elizaveta Vishnyakova  1

1 Université du Luxembourg, 6 rue Richard Coudenhove-Kalergi, 1359 Luxembourg 
Elizaveta Vishnyakova. The Splitting Problem for Complex Homogeneous Supermanifolds. Journal of Lie Theory, Tome 25 (2015) no. 2, pp. 459-476. http://geodesic.mathdoc.fr/item/JOLT_2015_25_2_a7/
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     title = {The {Splitting} {Problem} for {Complex} {Homogeneous} {Supermanifolds}},
     journal = {Journal of Lie Theory},
     pages = {459--476},
     year = {2015},
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     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2015_25_2_a7/}
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