Geodesic
The Lie Superalgebra of a Supermanifold
Janusz Grabowski1 ; Alexei Kotov2 ; Norbert Poncin2
1Polish Academy of Sciences, Institute of Mathematics, ul. Sniadeckich 8, 00-956 Warsaw, Poland
2Mathematics Research Unit, University of Luxembourg, 6, rue Richard Coudenhove-Kalergi, 1359 Luxembourg City, Luxembourg
Journal of Lie Theory, Tome 20 (2010) no. 4, pp. 739-749

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

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

Janusz Grabowski  1   ; Alexei Kotov  2   ; Norbert Poncin  2

1 Polish Academy of Sciences, Institute of Mathematics, ul. Sniadeckich 8, 00-956 Warsaw, Poland
2 Mathematics Research Unit, University of Luxembourg, 6, rue Richard Coudenhove-Kalergi, 1359 Luxembourg City, Luxembourg 
Janusz Grabowski; Alexei Kotov; Norbert Poncin. The Lie Superalgebra of a Supermanifold. Journal of Lie Theory, Tome 20 (2010) no. 4, pp. 739-749. http://geodesic.mathdoc.fr/item/JOLT_2010_20_4_a6/
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     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/JOLT_2010_20_4_a6/}
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