SOME RESULTS ON LIE ALGEBRAS FROM CONNECTIONS

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SOME RESULTS ON LIE ALGEBRAS FROM CONNECTIONS
JMMAFI, ISSN 2411-7188, Vol.6, 2023, pp.1-20
Auteur : PRINCY RANDRIAMBOLOLONDRANTOMALALA

[EN] In this paper, we consider a smooth manifold M of dimension n, T M de-
notes the tangent bundle of M without the null section. Our main goal is to see some
remarkable algebraic properties of the Lie algebra AΓ of vector fields on T M whose the
Lie derivatives vanish a Grifone’s connection Γ, those of the curvature nullity space of
Γ and those of the set of all Grifone’s connections on M, by global ways such as the
study of (m ≥ 2)-derivations, the Chevalley-Eilenberg cohomology, of the Lie algebras
generated by these considerations, and by local methods such that relations becoming
from system of partial differential equations between all elements of these Lie algebras
which permit their local forms to be well known. Especially we compute all (m ≥ 2)-
derivations, cohomology of the Lie algebra of infinitesimal automorphisms of Γ and of
its normalizer both sub-algebras of AΓ.
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