Splittable Lie Groups and Lie Algebras

We show that each Malʹcev splittable -Lie algebra (i.e., each -Lie algebra where ad( ) is splittable) with char = 0 may be realized as a splittable subalgebra of a gl(V), where V is a finite-dimensional vector space over , and that each Malʹcev splittable analytic subgroup of a GL(n, ), i.e., each subgroup whose Lie algebra is Malʹcev splittable, can be realized as an analytic splittable subgroup of a GL(m, ). Finally these results are applied to establish a necessary and sufficient condition for the exponential function of a Malʹcev splittable Lie group to be surjective.