Lattices of some solvable Lie groups and actions of products of affine groups
Tsuchiya, Nobuo ; Yamakawa, Aiko
Tohoku Math. J. (2), Tome 61 (2009) no. 1, p. 349-364 / Harvested from Project Euclid
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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.
Publié le : 2009-05-15
Classification:  Solvable Lie groups,  lattices,  homogeneous actions,  22E25,  22F30,  57S20 
@article{1255700199,
     author = {Tsuchiya, Nobuo and Yamakawa, Aiko},
     title = {Lattices of some solvable Lie groups and actions of products of affine groups},
     journal = {Tohoku Math. J. (2)},
     volume = {61},
     number = {1},
     year = {2009},
     pages = { 349-364},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1255700199}
}

Tsuchiya, Nobuo; Yamakawa, Aiko. Lattices of some solvable Lie groups and actions of products of affine groups. Tohoku Math. J. (2), Tome 61 (2009) no. 1, pp.  349-364. http://gdmltest.u-ga.fr/item/1255700199/