Geodesic
Lie Superalgebras of Differential Operators
Janusz Grabowski1 ; Alexei Kotov2, 3 ; Norbert Poncin2
1Polish Academy of Sciences, Institute of Mathematics, Sniadeckich 8 -- P.O. Box 21, 00-956 Warsaw, Poland
2Faculté des Sciences, University of Luxembourg, 6, rue Richard Coudenhove-Kalergi, 1359 Luxembourg City, Luxembourg
3Institute of Mathematics and Statistics, University of Tromso, 9037 Tromso, Norway
Journal of Lie Theory, Tome 23 (2013) no. 1, pp. 35-54

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

We describe explicitly Lie superalgebra isomorphisms between the Lie superalgebras of first-order superdifferential operators on supermanifolds, showing in particular that any such isomorphism induces a diffeomorphism of the supermanifolds. We also prove that the group of automorphisms of such a Lie superalgebra is a semi-direct product of the subgroup of automorphisms induced by the supermanifold diffeomorphisms and another subgroup which consists of automorphisms determined by even superdivergences. We prove the existence of such superdivergences on any supermanifold and we describe their local form.
Classification : 58A50, 17B40, 17B66, 13N10, 17B56
Mots-clés : Supermanifold, Lie superalgebra, differential operators, vector fields, automorphisms, Lie superalgebra cohomology, divergence

Janusz Grabowski  1   ; Alexei Kotov  2 , 3   ; Norbert Poncin  2

1 Polish Academy of Sciences, Institute of Mathematics, Sniadeckich 8 -- P.O. Box 21, 00-956 Warsaw, Poland
2 Faculté des Sciences, University of Luxembourg, 6, rue Richard Coudenhove-Kalergi, 1359 Luxembourg City, Luxembourg
3 Institute of Mathematics and Statistics, University of Tromso, 9037 Tromso, Norway 
Janusz Grabowski; Alexei Kotov; Norbert Poncin. Lie Superalgebras of Differential Operators. Journal of Lie Theory, Tome 23 (2013) no. 1, pp. 35-54. http://geodesic.mathdoc.fr/item/JOLT_2013_23_1_a1/
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     title = {Lie {Superalgebras} of {Differential} {Operators}},
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