On Levi subgroups and the Levi decomposition for groups definable in o-minimal structures

• Autorzy: Annalisa Conversano , Anand Pillay
• Języki publikacji: EN

Abstrakty

EN

We study analogues of the notions from Lie theory of Levi subgroup and Levi decomposition, in the case of groups G definable in an o-minimal expansion of a real closed field. With a rather strong definition of ind-definable semisimple subgroup, we prove that G has a unique maximal ind-definable semisimple subgroup S, up to conjugacy, and that G = R· S where R is the solvable radical of G. We also prove that any semisimple subalgebra of the Lie algebra of G corresponds to a unique ind-definable semisimple subgroup of G.

Kategorie tematyczne

• 03C64: Model theory of ordered structures; o-minimality
• 22E15: General properties and structure of real Lie groups

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2013
• Tom: 222
• Numer: 1
• Strony: 49-62

Daty

wydano

2013

Twórcy

autor

Annalisa Conversano

• Institute of Natural and Mathematical Sciences, Massey University, P/bag 102-904 NSMC, Auckland, NZ

autor

Anand Pillay

• Department of Pure Mathematics, University of Leeds, LS2 9JT Leeds, UK

Identyfikatory

DOI

10.4064/fm222-1-3