Accueil > Documentations scientifiques > Revues récentes > Journal de Mathématiques, Mathématiques&Applications Fondamentales et (...) > Volume 6 ,2023, ISSN : 2411-7188 > Some results on lie algebras from connections

  • Some results on lie algebras from connections
    JMMAFI, ISSN 2411-7188, Vol.6, 2023, pp.1-20


    [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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