Journal of Lie Theory 30 (2020), No. 1, 171--178
Copyright Heldermann Verlag 2020
Subsemigroups of Nilpotent Lie Groups
Fakultät für Mathematik, Universität Bielefeld, 33501 Bielefeld, Germany
Ernest B. Vinberg
Chair of Algebra, Dept. of Mechanics and Mathematics, Moscow State University, Moscow 119991, Russia
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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