Casamir operators; Classification; Equivariant symbol calculus; Modules of differential operators
Abstract :
[en] We prove the existence and uniqueness of a projectively equivariant symbol map (in the sense of Lecomte and Ovsienko) for the spaces D_p of differential operators transforming p-forms into functions, over R^n. As an application, we classify the Vect(M)-equivariant maps from D_p to D_q over a smooth manifold M, recovering and improving earlier results of N. Poncin. This provides the complete answer to a question raised by P. Lecomte about the extension of a certain intrinsic homotopy operator.
Disciplines :
Mathematics
Author, co-author :
Boniver, Fabien; Université de Liège - ULiège > Département de Mathématique > Département de Mathématique
Hansoul, Sarah ; Université de Liège - ULiège > Département de Mathématique > Département de Mathématique
Mathonet, Pierre ; Université de Liège - ULiège > Département de mathématique > Département de mathématique
Poncin, Norbert; Centre Universitaire de Luxembourg > Département de Mathématiques
Language :
English
Title :
Equivariant symbol calculus for differential operators acting on forms
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Bibliography
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Lecomte, P. B. A., Mathonet, P. and Tousset, E.: Comparison of some modules of the Lie algebra of vector fields, Indag. Math. (N.S.) 7(4) (1996), 461-471.
Lecomte, P. B. A. and Ovsienko, V. Yu.: Projectively equivariant symbol calculus, Lett. Math. Phys. 49(3) (1999), 173-196.
Lecomte, P. B. A.: On some sequence of graded Lie algebras associated to manifolds, Ann. Global Anal. Geom. 12(2) (1994), 183-192.
Mathonet, P.: Intertwining operators between some spaces of differential operators on a manifold, Comm. Algebra 27(2) (1999), 755-776.
Poncin, N.: Equivariant operators between spaces of differential operators from differential forms into functions, Preprint, Centre Universitaire de Luxembourg, 2002.
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