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Maximal semigroups in semi-simple Lie groups
Author(s):
Luiz
A. B.
San Martin
Journal:
Trans. Amer. Math. Soc.
353
(2001),
5165-5184.
MSC (2000):
Primary 20M20, 22E20, 22F30
Posted:
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  -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  -convex set.
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Additional Information:
Luiz
A. B.
San Martin
Affiliation:
Instituto de Matemática, Universidade Estadual de Campinas, Cx.Postal 6065, 13083-970 Campinas SP, Brasil
Email:
smartin@ime.unicamp.br
DOI:
10.1090/S0002-9947-01-02868-9
PII:
S 0002-9947(01)02868-9
Keywords:
Semigroups,
semi-simple Lie groups,
flag manifolds,
convexity
Received by editor(s):
March 18, 1999
Received by editor(s) in revised form:
March 29, 2001
Posted:
June 14, 2001
Additional Notes:
Research partially supported by CNPq grant n$^{\circ }$ $301060/94-0$.
Copyright of article:
Copyright
2001,
American Mathematical Society
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