6533b861fe1ef96bd12c5865
RESEARCH PRODUCT
The first Chevalley–Eilenberg Cohomology group of the Lie algebra on the transverse bundle of a decreasing family of foliations
Leila Lebtahisubject
Pure mathematicsFoliacions (Matemàtica)Group (mathematics)General Physics and AstronomyLie Àlgebres deQuotient space (linear algebra)CohomologyAlgebraTensor (intrinsic definition)Lie bracket of vector fieldsLie algebraVector fieldFiber bundleGeometry and TopologyMathematical PhysicsMathematicsdescription
Abstract 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 ≠ 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 , J Y ] = 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 ) ) .
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2010-12-01 | Journal of Geometry and Physics |