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Some lie algebras of vector fields and their derivations Case of partially classical type

Published online by Cambridge University Press:  22 January 2016

Yukihiro Kanie
Affiliation:
Department of Mathematics, Mie University
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Extract

Let be a smooth foliated manifold, and the Lie algebra of all leaf-tangent vector fields on M.

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1981

References

[1] Cartan, E., Les groupes de transformations continus, infinis, simples, Ann. Ecole Norm. Sup., 26 (1909), 93161.CrossRefGoogle Scholar
[2] Kanie, Y., Cohomologies of Lie algebras of vector fields with coefficients in adjoint representations; Hamiltonian case, Publ. RIMS., Kyoto Univ., 10 (1975), 737762.Google Scholar
[3] Kanie, Y., Cohomologies of Lie algebras of vector fields with coefficients in adjoint representations; Case of classical type, Publ. RIMS., Kyoto Univ., 11 (1975), 213245.CrossRefGoogle Scholar
[4] Kanie, Y., Cohomologies of vector fields of vector fields with coefficients in adjoint representations; Foliated case, Publ. RIMS., Kyoto Univ., 14 (1978), 487501.CrossRefGoogle Scholar
[5] Morimoto, T., On the intransitive Lie algebras whose transitive parts are infinite and primitive, J. Math. Soc. Japan, 29 (1977), 3565.CrossRefGoogle Scholar
[6] Nakanishi, N., Derivation algebra of infinite Lie algebras (unpublished).Google Scholar
[7] Reeb, G., Sur les certaines propriétés topologiques des variétés feuilletées, Act. Sci. Ind., Hermann, Paris, 1183 (1952), 83154.Google Scholar
[8] Singer, I. M. and Sternberg, S., On the infinite groups of Lie and Cartan, Part I (transitive case), J. Analyse Math., 15 (1965), 1114.CrossRefGoogle Scholar
[9] Takens, F., Derivations of vector fields, Comp. Math., 26 (1973), 151158.Google Scholar
[10] Weyl, H., The Classical Groups; their invariants and representation, Princeton Univ. Press, 2nd ed. (1946).Google Scholar
[11] Kanie, Y., Some Lie algebras of vector fields on foliated manifolds and their derivation algebras, to appear in Proc. Japan Acad. Google Scholar

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