LENTICULAR NONCOMMUTATIVE TORI

Abstract

Abstract:

All C-algebras of sections of locally trivial C-algebra bundles overQsi=1 Lki (ni) with fibres A! Mc(C) are constructed, under the assumption that every completely irra-tional noncommutative torus A! is realized as an inductive limit of circle algebras, where Lki (ni) are lens spaces. Let Lcd be a cd-homogeneous C-algebra overQsi=1 Lki (ni)×Tr+2 whose cd-homogeneous C-subalgebra restricted to the subspace Tr × T2 is realized as
C(Tr) A l d Mc(C), and of which no non-trivial matrix algebra can be factored out.The lenticular noncommutative torus Lcd is defined by twisting C(dTr+2) C(Zm−2)in Lcd C(Zm−2) by a totally skew multiplier ρ on dTr+2 × Zm−2. It is shown that Lcd Mp∞ is isomorphic to C(Qsi=1 Lki (ni))
AMcd(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 Lcd is not stablyisomorphic to C(Qs
i=1 Lki (ni)) A Mcd(C) if the cd-homogeneous C-subalgebra o fLcd restricted to some subspace Lki (ni) ?! Qsi=1 Lki (ni) is realized as the crossed productby the obvious non-trivial action of Zki on a cd ki -homogeneous C-algebra over S2ni+1 for ki an integer greater than 1.

Key words: Lens space, homogeneous C-algebra, C-algebra bundle, twisted group C-algebra, noncommutative torus, K-theory, UHF-algebra, Cuntz algebra

CLC Number:

46L87

Chun-Gil Park. LENTICULAR NONCOMMUTATIVE TORI[J].Acta mathematica scientia,Series B, 2003, 23(1): 83-94.

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