Preliminaries.- I. Generalities on Lattices.- II. Lattices in Nilpotent Lie Groups.- III. Lattices in Solvable Lie Groups.- IV. Polycyclic Groups and Arithmeticity of Lattices in Solvable Lie… Expand

Introduction. Let G be a connected semi-simple Lie group and r a discrete subgroup such that the quotient G/r is compact. Let po be a finite dimensional representation of G. Our aim in this paper, is… Expand

Let G be an algebraic group defined, over Q. We assume that G c GL(n, C). Let Gz = G n SL(n, Z), and for any ideal accZ, let Ga =G SL(n, a) where SL(n, a) is the kernel of the natural map SL(n, Z) >… Expand

(1) a proof that every unitary representation with non-zero cohomology, see Betel [2], occurs in L ~ ( I ~ S O (n, 1)) for a suitable uniform F, thereby proving for the group SO (n, 1) a conjecture… Expand

Let G be a semisimple Lie group of rank ⩾2 and Γ an irreducible lattice. Γ has two natural metrics: a metric inherited from a Riemannian metric on the ambient Lie group and a word metric defined with… Expand

A hydraulic engine for transforming the energy of a flowing current of water into a pressure head of water. The engine is mounted on a platform supported by floats and fitted with a series of paddles… Expand