Geodesic
The Splitting Problem for Complex Homogeneous Supermanifolds
Journal of Lie theory, Tome 25 (2015) no. 2, pp. 459-476
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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.
Classification : 51P05, 53Z05, 32M10
Mots-clés : Lie supergroup, complex homogeneous supermanifold 
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     author = {E. Vishnyakova},
     title = {The {Splitting} {Problem} for {Complex} {Homogeneous} {Supermanifolds}},
     journal = {Journal of Lie theory},
     pages = {459--476},
     year = {2015},
     volume = {25},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JLT_2015_25_2_JLT_2015_25_2_a7/}
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E. 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/JLT_2015_25_2_JLT_2015_25_2_a7/