On central extensions and definably compact groups in o-minimal structures

Ehud Hrushovski, Ya'acov Peterzil, Anand Pillay

Research output: Contribution to journalArticlepeer-review

Abstract

We prove several structural results on definable, definably compact groups G in o-minimal expansions of real closed fields such as (i) G is definably an almost direct product of a semisimple group and a commutative group, (ii) (G,·) is elementarily equivalent to (G/G00,·). We also prove results on the internality of finite covers of G in an o-minimal environment, as well as deducing the full compact domination conjecture for definably compact groups from the semisimple and commutative cases which were already settled.These results depend on key theorems about the interpretability of central and finite extensions of definable groups, in the o-minimal context. These methods and others also yield interpretability results for universal covers of arbitrary definable real Lie groups.

Original languageEnglish
Pages (from-to)71-106
Number of pages36
JournalJournal of Algebra
Volume327
Issue number1
DOIs
StatePublished - 1 Feb 2011

Bibliographical note

Funding Information:
✩ The first author thanks ISF grant 1048-078, and travel funds from an EPSRC grant. The third author thanks the European Commission (Marie Curie Excellence chair), the EPSRC (grant EP/F009712/1), as well as Université Paris-Sud 11. All authors thank the Marie Curie Modnet network for facilitating the collaboration. * Corresponding author. E-mail addresses: ehud@math.huji.ac.il (E. Hrushovski), kobi@math.haifa.ac.il (Y. Peterzil), pillay@maths.Leeds.ac.uk (A. Pillay).

Keywords

  • Central extensions
  • Compact domination
  • Definably compact
  • O-minimality
  • Semialgebraic groups
  • Universal covers

ASJC Scopus subject areas

  • Algebra and Number Theory

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