 Lie algebra bundle

In mathematics, a weak Lie algebra bundle

is a vector bundle formula_2 over a base space "X" together with a morphism

which induces a Lie algebra structure on each fibre formula_4.A Lie algebra bundle formula_5 is a vector bundle in which
each fibre is a Lie algebra and for every "x" in "X", there is an open set formula_6 containing "x", a Lie algebra "L" and a homeomorphism

such that

is a Lie algebra isomorphism.