Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Maximal semigroups in semi-simple Lie groups


Author: Luiz A. B. San Martin
Journal: Trans. Amer. Math. Soc. 353 (2001), 5165-5184
MSC (2000): Primary 20M20, 22E20, 22F30
Published electronically: June 14, 2001
MathSciNet review: 1852099
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 20M20, 22E20, 22F30

Retrieve articles in all journals with MSC (2000): 20M20, 22E20, 22F30


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: http://dx.doi.org/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
Published electronically: June 14, 2001
Additional Notes: Research partially supported by CNPq grant n$^{∘}$ $301060/94-0$.
Article copyright: © Copyright 2001 American Mathematical Society