Journal of Lie Theory Volume 6 (1996) 23–51 R1996 Heldermann Verlag

Non-Associative Local Lie Groups

Peter J. Olver

Communicated by Karl H. Hofmann

Abstract. 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.

Peter J. Olver, School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA olver@ima.umn.edu

Received December 11, 1995 and in final form June 10, 1996

ISSN 0949–5932 / $2.50 R Heldermann Verlag