Tohoku Mathematical Journal

Lattices of some solvable Lie groups and actions of products of affine groups

Nobuo Tsuchiya and Aiko Yamakawa

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Abstract

We consider solvable Lie groups which are isomorphic to unimodularizations of products of affine groups. It is shown that a lattice of such a Lie group is determined, up to commensurability, by a totally real algebraic number field. We also show that the outer automorphism group of the lattice is represented faithfully in the automorphism group of the number field. As an application, we obtain a classification of codimension one, volume preserving, locally free actions of products of affine groups.

Article information

Source
Tohoku Math. J. (2), Volume 61, Number 3 (2009), 349-364.

Dates
First available in Project Euclid: 16 October 2009

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1255700199

Digital Object Identifier
doi:10.2748/tmj/1255700199

Mathematical Reviews number (MathSciNet)
MR2568259

Zentralblatt MATH identifier
1181.22014

Subjects
Primary: 22E25: Nilpotent and solvable Lie groups
Secondary: 22F30: Homogeneous spaces {For general actions on manifolds or preserving geometrical structures, see 57M60, 57Sxx; for discrete subgroups of Lie groups, see especially 22E40} 57S20: Noncompact Lie groups of transformations

Keywords
Solvable Lie groups lattices homogeneous actions

Citation

Tsuchiya, Nobuo; Yamakawa, Aiko. Lattices of some solvable Lie groups and actions of products of affine groups. Tohoku Math. J. (2) 61 (2009), no. 3, 349--364. doi:10.2748/tmj/1255700199. https://projecteuclid.org/euclid.tmj/1255700199


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