Maximal semigroups in semi-simple Lie groups

San Martin, Luiz

doi:10.1090/S0002-9947-01-02868-9

Maximal semigroups in semi-simple Lie groups
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by Luiz A. B. San Martin

Trans. Amer. Math. Soc. 353 (2001), 5165-5184

DOI: https://doi.org/10.1090/S0002-9947-01-02868-9

Published electronically: June 14, 2001

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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 $\mathcal {B}$-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 $\mathcal {B}$-convex set.

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