LENTICULAR NONCOMMUTATIVE TORI

Abstract

All C*-algebras of sections of locally trivial C*-algebra bundles over Πi=1sLki(ni) with fibres Aω⊗Mc(C) are constructed, under the assumption that every completely irrational noncommutative torus Aw is realized as an inductive limit of circle algebras, where Lki (ni) are lens spaces. Let Lcd be a cd-homogeneous C*-algebra over Πi=1sLki(ni)×Tτ+2 whose cd-homogeneous C*-subalgebra restricted to the subspace Tτ+T2 is realized as C(Tτ)⊗A1d⊗Mc(C), and of which no non-trivial matrix algebra can be factored out. The lenticular noncommutative torus Lρcd is defined by twisting C*(Tr+2^)⊗C*(Zm-2) in Lcd⊗C*(Zm-2) by a totally skew multiplier ρ on Tr+2^×Zm-2. It is shown that Lcd⊗Mp∞ is isomorphic to C(Πi=1sLki(ni))⊗Aρ⊗Mcd(C)⊗Mp∞ if and only if the set of prime factors of cd is a subset of the set of prime factors of p, and that Lρcd is not stably isomorphic to C(Πi=1s Lki(ni))⊗Aρ⊗Mcd(C) if the cd-homogeneous C*-subalgebra of Lρcd restricted to some subspace Lki(ni)↪Πi=1sLki(ni) is realized as the crossed product by the obvious non-trivial action of Zki on a cdki-homogeneous C*-algebra over S2ni+1 for ki an integer greater than 1.