Abstract
The maximal semigroups with nonempty interior in a semi-simple Lie group with finite' center are characterized as compression semigroups of subsets in the flag manifolds of the group. For this purpose a convexity theory, called here B-convexity, based on the open Bruhat cells is developed. It turns out that a semigroup with nonempty interior is maximal if and only if it is the compression semigroup of the interior of a B-convex set.
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