Lie algebra bundle

In mathematics, a weak Lie algebra bundle In mathematics, a weak Lie algebra bundle is a vector bundle ξ {displaystyle xi ,} over a base space X together with a morphism which induces a Lie algebra structure on each fibre ξ x {displaystyle xi _{x},} . A Lie algebra bundle ξ = ( ξ , p , X ) {displaystyle xi =(xi ,p,X),} is a vector bundle in whicheach fibre is a Lie algebra and for every x in X, there is an open set U {displaystyle U} containing x, a Lie algebra L and a homeomorphism