The product of a exponential of the compact algebra with that of the non-compact algebra recovers a simple Lie from its algebra
= The product of a exponential of the compact algebra with that of the non-compact algebra recovers a simple Lie from its algebra
Example at: <Lie Groups, Physics, and Geometry by Robert Gilmore (2008)> Chapter 7 "EXPonentiation".
Furthermore, the non-<compact> part is always <isomorphic> to <\R^n>, only the non-compact part can have more interesting structure.