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)

 

Simple algebraic and semialgebraic groups over real closed fields


Authors: Ya'acov Peterzil, Anand Pillay and Sergei Starchenko
Journal: Trans. Amer. Math. Soc. 352 (2000), 4421-4450
MSC (1991): Primary 03C64, 22E15, 20G20; Secondary 12J15
Published electronically: June 13, 2000
MathSciNet review: 1779482
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We continue the investigation of infinite, definably simple groups which are definable in o-minimal structures. In Definably simple groups in o-minimal structures, we showed that every such group is a semialgebraic group over a real closed field. Our main result here, stated in a model theoretic language, is that every such group is either bi-interpretable with an algebraically closed field of characteristic zero (when the group is stable) or with a real closed field (when the group is unstable). It follows that every abstract isomorphism between two unstable groups as above is a composition of a semialgebraic map with a field isomorphism. We discuss connections to theorems of Freudenthal, Borel-Tits and Weisfeiler on automorphisms of real Lie groups and simple algebraic groups over real closed fields.


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


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 03C64, 22E15, 20G20, 12J15

Retrieve articles in all journals with MSC (1991): 03C64, 22E15, 20G20, 12J15


Additional Information

Ya'acov Peterzil
Affiliation: Department of Mathematics and Computer Science, Haifa University, Haifa, Israel
Email: kobi@mathcs2.haifa.ac.il

Anand Pillay
Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green St., Urbana, Illinois 61801
Email: pillay@math.uiuc.edu

Sergei Starchenko
Affiliation: Department of Mathematics, University of Notre Dame, CCMB, Notre Dame, Indiana 46556
Email: starchenko.1@nd.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-00-02667-2
PII: S 0002-9947(00)02667-2
Received by editor(s): February 25, 1998
Published electronically: June 13, 2000
Additional Notes: We thank the referee for valuable comments
The second and the third authors were partially supported by NSF
Article copyright: © Copyright 2000 American Mathematical Society