Journal of Lie Theory 19 (2009), No. 4, 685--695
Copyright Heldermann Verlag 2009
Locally Compact Contractive Local Groups
Lou van den Dries
Dept. of Mathematics, University of Illinois, 1409 W. Green Street, Urbana, IL 61801, U.S.A.
Dept. of Mathematics, University of California, 520 Portola Plaza, Los Angeles, CA 90095-1555, U.S.A.
We study locally compact contractive local groups, that is, locally compact local groups with a contractive pseudo-automorphism. We prove that if such an object is locally connected, then it is locally isomorphic to a Lie group. We also prove a related structure theorem for locally compact contractive local groups which are not necessarily locally connected. These results are local analogues of theorems for locally compact contractive groups.
Keywords: Locally compact local groups, contractive pseudo-automorphism, Mal'cev's theorem.
MSC: 22D05, 22E05.
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