Journal of Lie Theory 30 (2020), No. 1, 171--178
Copyright Heldermann Verlag 2020
Subsemigroups of Nilpotent Lie Groups
Herbert Abels
Fakultät für Mathematik, Universität Bielefeld, 33501 Bielefeld, Germany
abels@math.uni-bielefeld.de
Ernest B. Vinberg
Chair of Algebra, Dept. of Mechanics and Mathematics, Moscow State University, Moscow 119991, Russia
evinberg@gmail.com
For a closed subsemigroup S of a simply connected nilpotent Lie group G, we prove that either S is a subgroup, or there is an epimorphism f from G to the reals R such that f(s) ≥ 0 for all s of S.
Keywords: Topological group, semigroup, nilpotent Lie group.
MSC: 22E25, 20M20.
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