Tohoku Mathematical Journal
2009
September
SECOND SERIES VOL. 61, NO. 3

Tohoku Math. J.
61 (2009), 349-364

Title LATTICES OF SOME SOLVABLE LIE GROUPS AND ACTIONS OF PRODUCTS OF AFFINE GROUPS

Author Nobuo Tsuchiya and Aiko Yamakawa

(Received January 17, 2008, revised March 9, 2009)
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.

2000 Mathematics Subject Classification. Primary 22E25; Secondary 22F30, 57S20.
Key words and phrases. Solvable Lie groups, lattices, homogeneous actions.

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