Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

The generation of nonlinear equivariant differential operators
HTML articles powered by AMS MathViewer

by Robert Delver PDF
Proc. Amer. Math. Soc. 77 (1979), 401-408 Request permission

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.
References
  • Salomon Bochner and Deane Montgomery, Groups of differentiable and real or complex analytic transformations, Ann. of Math. (2) 46 (1945), 685–694. MR 14102, DOI 10.2307/1969204
    • N. Bourbaki, Lie groups and Lie algebras, Part I, Addison-Wesley, Reading, Mass., 1975.
  • Robert Delver, Equivariant differential operators of a Lie group, Transformation groups (Proc. Conf., Univ. Newcastle upon Tyne, Newcastle upon Tyne, 1976) London Math. Soc. Lecture Note Series, No. 26, Cambridge Univ. Press, Cambridge, 1977, pp. 40–50. MR 0474438
  • J. Dieudonné, Treatise on analysis. Vol. III, Pure and Applied Mathematics, Vol. 10-III, Academic Press, New York-London, 1972. Translated from the French by I. G. MacDonald. MR 0350769
  • Werner Greub, Stephen Halperin, and Ray Vanstone, Connections, curvature, and cohomology, Pure and Applied Mathematics, Vol. 47-III, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1976. Volume III: Cohomology of principal bundles and homogeneous spaces. MR 0400275
  • Dale Husemoller, Fibre bundles, 2nd ed., Graduate Texts in Mathematics, No. 20, Springer-Verlag, New York-Heidelberg, 1975. MR 0370578
  • A. Kumpera, Invariants différentiels d’un pseudogroupe de Lie, Géométrie différentielle (Colloq., Univ. Santiago de Compostela, Santiago de Compostela, 1972) Lecture Notes in Math., Vol. 392, Springer, Berlin, 1974, pp. 121–162 (French). MR 0407910
    • 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. 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.
  • Gerald W. Schwarz, Smooth functions invariant under the action of a compact Lie group, Topology 14 (1975), 63–68. MR 370643, DOI 10.1016/0040-9383(75)90036-1
  • Ar. Tresse, Sur les invariants différentiels des groupes continus de transformations, Acta Math. 18 (1894), no. 1, 1–3 (French). MR 1554846, DOI 10.1007/BF02418270
  • V. S. Varadarajan, Lie groups, Lie algebras, and their representations, Prentice-Hall Series in Modern Analysis, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1974. MR 0376938
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 58G99
  • Retrieve articles in all journals with MSC: 58G99
Additional Information
  • © Copyright 1979 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 77 (1979), 401-408
  • MSC: Primary 58G99
  • DOI: https://doi.org/10.1090/S0002-9939-1979-0545604-X
  • MathSciNet review: 545604