Geodesic
The Lie Superalgebra of a Supermanifold
Journal of Lie theory, Tome 20 (2010) no. 4, pp. 739-749 Cet article a éte moissonné depuis la source Heldermann Verlag

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We prove a "superversion" of Shanks and Pursell's classical result stating that any isomorphism of the Lie algebras of compactly supported vector fields is implemented by a diffeomorphism of underlying manifolds. We thus provide a Lie algebraic characterization of supermanifolds and describe explicitly isomorphisms of the Lie superalgebras of supervector fields on supermanifolds.
Classification : 58A50, 17B66, 14F05, 17B70, 17B40
Mots-clés : Superalgebra, noncommutative space, supermanifold, graded manifold, super vector field, graded Lie algebra 
@article{JLT_2010_20_4_JLT_2010_20_4_a6,
     author = {J. Grabowski and A. Kotov and N. Poncin },
     title = {The {Lie} {Superalgebra} of a {Supermanifold}},
     journal = {Journal of Lie theory},
     pages = {739--749},
     year = {2010},
     volume = {20},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JLT_2010_20_4_JLT_2010_20_4_a6/}
}
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J. Grabowski; A. Kotov; N. Poncin . The Lie Superalgebra of a Supermanifold. Journal of Lie theory, Tome 20 (2010) no. 4, pp. 739-749. http://geodesic.mathdoc.fr/item/JLT_2010_20_4_JLT_2010_20_4_a6/