Lattices of some solvable Lie groups and actions of products of affine groups
Nobuo Tsuchiya and Aiko Yamakawa
Source: Tohoku Math. J. (2) Volume 61, Number 3
(2009), 349-364.
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.
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Permanent link to this document: http://projecteuclid.org/euclid.tmj/1255700199
Digital Object Identifier: doi:10.2748/tmj/1255700199
Zentralblatt MATH identifier: 05650400
Mathematical Reviews number (MathSciNet): MR2568259
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Digital Object Identifier: doi:10.2748/tmj/1178207480
Project Euclid: euclid.tmj/1178207480
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