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On the Classification of Lie Pseudo-Algebras

  • Ngö van Quê (a1)

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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.

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References

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1. Cartan, E., Les groupes de transformations continus infinis, simples, Ann. Sri. Ecole Norm. Sup., Paris, 1909.
2. Guillemin, V. W., Quillen, D., and Sternberg, S., The classification of the irreducible complex algebras of infinite type, J. Analyse Math. 18 (1967), 107112.
3. Kobayashi, S. and Nagano, I., On filtered Lie algebras and geometric structures. III, J. Math. Mech. 14 (1965), 679706.
4. Matsushima, Y., Sur les algèbres de Lie linéaires semi-involutives, Colloque de topologie de Strasbourg, 1954-1955 (Institut de mathématique, Université de Strasbourg).
5. Ngö van, Que, Du prolongement des espaces fibres et des structures infinitésimales, Ann. Inst. Fourier (Grenoble) 17 (1967), fasc. 1, 157223.
6. Singer, I. M. and Sternberg, S., The infinite groups of Lie and Cartan. I, The transitive groups, J. Analyse Math. 15 (1965), 1114.
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On the Classification of Lie Pseudo-Algebras

  • Ngö van Quê (a1)

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