Construction and investigation of lattices with matrix groups
Gabriele Nebe · Contemporary mathematics - American Mathematical Society · 1999
this paper, one may use the finite matrix groups to construct nice lattices and to deduce properties of the invariant lattices. The rational normalizer NQ := N GLd (Q) (G) of a finite subgroup G of GL d (Q) plays an important role in the investigation of G-invariant lattices, since NQ acts on Z(G) and on F(G). In particular if G is uniform, which means that F(G) = QF has dimension 1, the elements in NQ induce similarities of F . Such similarities can be used to construct overlattices of tensor products as defined in section 2.