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.
vddries@illinois.edu
Isaac Goldbring
Dept. of Mathematics, University of California, 520 Portola Plaza, Los Angeles, CA 90095-1555, U.S.A.
isaac@math.ucla.edu
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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