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The first Chevalley-Eilenberg cohomology group of the Lie algebra on the transverse bundle of a decreasing family of foliations

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	Lebtahi, Leila
	This document is a artículoDate2010
	Este documento está disponible también en : http://hdl.handle.net/10550/57770
	In [L. Lebtahi, Lie algebra on the transverse bundle of a decreasing family of foliations, J. Geom. Phys. 60 (2010), 122-133], we defined the transverse bundle V^k to a decreasing family of k foliations F_i on a manifold M. We have shown that there exists a (1,1) tensor J of V^k such that Jk≠0, J^(k+1) = 0 and we defined by L_J(V^k) the Lie Algebra of vector fields X on V^k such that, for each vector field Y on V^k, [X,JY]=J[X,Y]. In this note, we study the first Chevalley-Eilenberg Cohomology Group, i.e. the quotient space of derivations of L_J(V^k) by the subspace of inner derivations, denoted by H^1(L_J(V^k)).
	Lebtahi, Leila 2010 The first Chevalley-Eilenberg cohomology group of the Lie algebra on the transverse bundle of a decreasing family of foliations Journal of Geometry and Physics 60 12 2011 2023
	http://dx.doi.org/10.1016/j.geomphys.2010.08.004