Generalized non-commutative tori

Chun-Gil Park

Chun-Gil Park

Studia Mathematica, Tome 151 (2002), p. 101-108 / Harvested from The Polish Digital Mathematics Library

Résumé

The generalized non-commutative torus $T_{ϱ}^{k}$ of rank n is defined by the crossed product $A_{m / k} \times_{α ₃} ℤ \times_{α ₄} . . . \times_{α ₙ} ℤ$ , where the actions $α_{i}$ of ℤ on the fibre $M_{k} (ℂ)$ of a rational rotation algebra $A_{m / k}$ are trivial, and $C * (k ℤ \times k ℤ) \times_{α ₃} ℤ \times_{α ₄} . . . \times_{α ₙ} ℤ$ is a non-commutative torus $A_{ϱ}$ . It is shown that $T_{ϱ}^{k}$ is strongly Morita equivalent to $A_{ϱ}$ , and that $T_{ϱ}^{k} \otimes M_{p^{\infty}}$ is isomorphic to $A_{ϱ} \otimes M_{k} (ℂ) \otimes M_{p^{\infty}}$ if and only if the set of prime factors of k is a subset of the set of prime factors of p.

Publié le : 2002-01-01

Zbl 0990.46044

EUDML-ID : urn:eudml:doc:284857

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     title = {Generalized non-commutative tori},
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     volume = {151},
     year = {2002},
     pages = {101-108},
     zbl = {0990.46044},
     language = {en},
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Chun-Gil Park. Generalized non-commutative tori. Studia Mathematica, Tome 151 (2002) pp. 101-108. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm149-2-1/