$C^\ast$-algebras from Anzai flows and their $K$-groups

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dc.creatorReihani, Kamran
dc.creatorMilnes, Paul
dc.date2003-11-24
dc.date.accessioned2026-07-07T05:03:13Z
dc.date.available2026-07-07T05:03:13Z
dc.descriptionWe study the $C^{*}$-algebra $\mathcal{A}_{n,θ}$ generated by the Anzai flow on the $n$-dimensional torus $\mathbb{T}^n$. It is proved that this algebra is a simple quotient of the group $C^{*}$-algebra of a lattice subgroup $\mathfrak{D}_n$ of a $(n+2)$-dimensional connected simply connected nilpotent Lie group $F_n$ whose corresponding Lie algebra is the generic filiform Lie algebra $\mathfrak{f}_{n}$. Other simple infinite dimensional quotients of $C^{*}(\mathfrak{D}_n)$ are also characterized and represented as matrix algebras over simple affine Furstenberg transformation group $C^*$-algebras of the lower dimensional tori. The $K$-groups of the $\mathcal{A}_{n,θ}$ and other simple quotients of $C^{*}(\mathfrak{D}_n)$ are studied, the Pimsner-Voiculescu 6-term exact sequence being a useful tool. The rank of the $K$-groups of $\mathcal{A}_{n,θ}$ is studied as explicitly as possible, and is proved to be the same as for more general transformation group $C^*$-algebras of $\mathbb{T}^n$ including the Furstenberg transformation group \text{$C^*$-algebras} $A_{F_{f,θ}}$. An error (about these $K$-groups) in the literature is addressed.
dc.description45 pages, 1 table, LaTex2e
dc.identifierhttps://arxiv.org/abs/math/0311425
dc.identifierhttp://arxiv.org/abs/math/0311425
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/69326
dc.subjectOperator Algebras
dc.subjectK-Theory and Homology
dc.subject22D25 (primary); 46L80 (secondary)
dc.title$C^\ast$-algebras from Anzai flows and their $K$-groups
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