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The generation of nonlinear equivariant differential operators

Author: Robert Delver
Journal: Proc. Amer. Math. Soc. 77 (1979), 401-408
MSC: Primary 58G99
MathSciNet review: 545604
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Abstract: Finite generation results are given for the set of smooth nonlinear differential operators: $ {C^\infty }(M,N) \to {C^\infty }(M,{\mathbf{R}})$ of order $ \leqslant k$ which are equivariant with respect to the action of a Lie group on the base manifold M.

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  • [1] Salomon Bochner and Deane Montgomery, Groups of differentiable and real or complex analytic transformations, Ann. of Math. (2) 46 (1945), 685–694. MR 0014102,
  • [2] N. Bourbaki, Lie groups and Lie algebras, Part I, Addison-Wesley, Reading, Mass., 1975.
  • [3] Robert Delver, Equivariant differential operators of a Lie group, Transformation groups (Proc. Conf., Univ. Newcastle upon Tyne, Newcastle upon Tyne, 1976) Cambridge Univ. Press, Cambridge, 1977, pp. 40–50. London Math. Soc. Lecture Note Series, No. 26. MR 0474438
  • [4] J. Dieudonné, Treatise on analysis. Vol. III, Academic Press, New York-London, 1972. Translated from the French by I. G. MacDonald; Pure and Applied Mathematics, Vol. 10-III. MR 0350769
  • [5] Werner Greub, Stephen Halperin, and Ray Vanstone, Connections, curvature, and cohomology, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1976. Volume III: Cohomology of principal bundles and homogeneous spaces; Pure and Applied Mathematics, Vol. 47-III. MR 0400275
  • [6] Dale Husemoller, Fibre bundles, 2nd ed., Springer-Verlag, New York-Heidelberg, 1975. Graduate Texts in Mathematics, No. 20. MR 0370578
  • [7] A. Kumpera, Invariants différentiels d’un pseudogroupe de Lie. II, J. Differential Geometry 10 (1975), no. 3, 347–416. MR 0407912
  • [8] S. Lie, Allgemeine Untersuchungen über Differentialgleichungen die eine kontinuierliche, endliche Gruppe gestatten, Math. Ann. 25 (1885), 77-151; Gesammete Abhandlungen, Bd. VI, Teubner, Leipzig, 1927, 139-223.
  • [9] R. S. Palais, Slices and equivariant imbeddings, Seminar in Transformation Groups, Chapter VIII, Ann. of Math. Studies, no. 46, Princeton Univ. Press, Princeton, N.J., 1968.
  • [10] Gerald W. Schwarz, Smooth functions invariant under the action of a compact Lie group, Topology 14 (1975), 63–68. MR 0370643,
  • [11] Ar. Tresse, Sur les invariants différentiels des groupes continus de transformations, Acta Math. 18 (1894), no. 1, 1–3 (French). MR 1554846,
  • [12] V. S. Varadarajan, Lie groups, Lie algebras, and their representations, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1974. Prentice-Hall Series in Modern Analysis. MR 0376938

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Keywords: Equivariant differential operators, transformation groups, differential invariants
Article copyright: © Copyright 1979 American Mathematical Society

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