Some semigroups on a manifold with boundary

Hanson, T. H. McH.

doi:10.1090/S0002-9939-1970-0263055-4

Some semigroups on a manifold with boundary

Author: T. H. McH. Hanson
Journal: Proc. Amer. Math. Soc. 25 (1970), 830-835
MSC: Primary 54.80; Secondary 22.00
DOI: https://doi.org/10.1090/S0002-9939-1970-0263055-4
MathSciNet review: 0263055
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Abstract: In this paper, $S$ is an abelian semigroup on an ${\text {n}}$-dimensional simply connected manifold with boundary whose interior is a dense, simply connected, connected Lie group. We also assume there is a vector semigroup $V_k^ -$ in $S$ such that the interior of $S$ misses the boundary of $V_k^ -$, and such that $(S - G{L_k})/{V_k}$ is a group. It is shown that if $k = n$, then $S$ is iseomorphic to $V_n^ -$, and if $k = 1,2$, or $n - 1$, then $S$ is iseomorphic to ${V_{n - k}} \times V_k^ -$.

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