Analysis on discrete cocompact subgroups of the generic filiform Lie groups
The standard filiform Lie group \({\mathcal F}_n\) contains a canonical lattice \({\mathcal D}_n\) given by integer coordinates. The current paper studies representations of the \(C^*\)-algebra \({\mathcal A}_n\) of \({\mathcal D}_n\). There are natural faithful representations on \(L^2\) of the \(n\)-dimensional torus, given by Anzai flows. There are also non-faithful representations which are given by matrix algebras over simple affine Furstenberg transformation groups \(C^*\) algebras of lower dimensional tori.
scientific article; zbMATH DE number 5082282