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

卷:60

Article

Lebtahi, Leila

关键词: Foliations;    Fiber bundles;    Lie algebra;    Derivation;    Cohomology group;   

DOI  :  10.1016/j.geomphys.2010.08.004

来源: Elsevier

【 摘 要 】

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 J(k) not equal 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))). (C) 2010 Elsevier B.V. All rights reserved.

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