A Zariski Dense and a Free Subgroup of Г

Abstract

In this section we explicitly construct a Zariski dense subgroup and, semi-explicitly, a free subgroup of Г. It suffices to construct such subgroups in the norm-one group of any order because, if Λ₁, Λ₂ are orders and Г₁ ⊂ Λ ^×₁ is Zariski dense (free), then so is Г₁ ∩ Λ ^×₂ . We shall use explicit matrix representations of Г, which arise from the realization of D as a cyclic crossed product, and begin by recalling this construction.