Abstract
It is well known that in a reductive group, the Borel subgroup is a product of the maximal torus and the one-dimensional positive root subgroups. The purpose of this paper is to find an analog of this result for reductive monoids. Via a study of reductive monoids of semisimple rank 1, we introduce the concept of root semigroups. By analyzing the associated root elements in the Renner monoid, we show that the closure of the Borel subgroup is generated by the maximal torus and positive root semigroups. Along the way we generalize the Jordan decomposition of algebraic groups to reductive monoids.
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