A general method for constructing local Lie groups which are not contained in any global Lie group is described. These examples fail to satisfy the global associativity axiom which, by a theorem of Mal'cev, is necessary and sufficient for globalizability. Furthermore, we prove that every local Lie group can be characterized by such a covering construction, thereby generalizing Cartan's global version of the Third Fundamental Theorem of Lie.
|Original language||English (US)|
|Number of pages||29|
|Journal||Journal of Lie Theory|
|State||Published - Dec 1 1996|