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On the Classification of Lie Pseudo-Algebras

Published online by Cambridge University Press:  20 November 2018

Ngö van Quê
Ngö van Quê*
Affiliation:
Université de Montréal, Montréal, Québec
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For every ( differentiable) bundle E over a manifold M, Jk(E) denotes the set of all k-jets of local (differentiable) sections of the bundle E. Jk(E) is a bundle over M such that if X is a section of E, then

is a (differentiable) section of Jk(E). If E is a vector bundle, Jk(E) is a vector bundle and we have the canonical exact sequence of vector bundles

where Sk(T*) is the symmetric Whitney tensor product of the cotangent vector bundle T* of M. and π is the canonical morphism which associates to each k-jet of section its jet of inferior order.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 22 , Issue 5 , 01 October 1970 , pp. 905 - 915
Copyright
Copyright © Canadian Mathematical Society 1970

References

1. Cartan, E., Les groupes de transformations continus infinis, simples, Ann. Sri. Ecole Norm. Sup., Paris, 1909.Google Scholar
2. Guillemin, V. W., Quillen, D., and Sternberg, S., The classification of the irreducible complex algebras of infinite type, J. Analyse Math. 18 (1967), 107–112.Google Scholar
3. Kobayashi, S. and Nagano, I., On filtered Lie algebras and geometric structures. III, J. Math. Mech. 14 (1965), 679–706.Google Scholar
4. Matsushima, Y., Sur les algèbres de Lie linéaires semi-involutives, Colloque de topologie de Strasbourg, 1954-1955 (Institut de mathématique, Université de Strasbourg).Google Scholar
5. Ngö van, Que, Du prolongement des espaces fibres et des structures infinitésimales, Ann. Inst. Fourier (Grenoble) 17 (1967), fasc. 1, 157–223.Google Scholar
6. Singer, I. M. and Sternberg, S., The infinite groups of Lie and Cartan. I, The transitive groups, J. Analyse Math. 15 (1965), 1–114.Google Scholar