Generalized non-commutative tori

Chun-Gil Park. "Generalized non-commutative tori." Studia Mathematica 149.2 (2002): 101-108. <http://eudml.org/doc/284857>.

@article{Chun2002,
abstract = {The generalized non-commutative torus $T_\{ϱ\}^\{k\}$ of rank n is defined by the crossed product $A_\{m/k\} ×_\{α₃\} ℤ ×_\{α₄\}... ×_\{αₙ\} ℤ$, where the actions $α_\{i\}$ of ℤ on the fibre $M_\{k\}(ℂ)$ of a rational rotation algebra $A_\{m/k\}$ are trivial, and $C*(kℤ × kℤ) ×_\{α₃\} ℤ ×_\{α₄\} ... ×_\{αₙ\} ℤ$ is a non-commutative torus $A_\{ϱ\}$. It is shown that $T^\{k\}_\{ϱ\}$ is strongly Morita equivalent to $A_\{ϱ\}$, and that $T_\{ϱ\}^\{k\} ⊗ M_\{p^\{∞\}\}$ is isomorphic to $A_\{ϱ\} ⊗ M_\{k\}(ℂ) ⊗ M_\{p^\{∞\}\}$ if and only if the set of prime factors of k is a subset of the set of prime factors of p.},
author = {Chun-Gil Park},
journal = {Studia Mathematica},
keywords = {non-commutative torus; equivalence bimodule; circle algebra; real rank 0; crossed product; UHF-algebra; Cuntz algebra; fibre; strongly Morita equivalent; prime factors},
language = {eng},
number = {2},
pages = {101-108},
title = {Generalized non-commutative tori},
url = {http://eudml.org/doc/284857},
volume = {149},
year = {2002},
}

TY - JOUR
AU - Chun-Gil Park
TI - Generalized non-commutative tori
JO - Studia Mathematica
PY - 2002
VL - 149
IS - 2
SP - 101
EP - 108
AB - The generalized non-commutative torus $T_{ϱ}^{k}$ of rank n is defined by the crossed product $A_{m/k} ×_{α₃} ℤ ×_{α₄}... ×_{αₙ} ℤ$, where the actions $α_{i}$ of ℤ on the fibre $M_{k}(ℂ)$ of a rational rotation algebra $A_{m/k}$ are trivial, and $C*(kℤ × kℤ) ×_{α₃} ℤ ×_{α₄} ... ×_{αₙ} ℤ$ is a non-commutative torus $A_{ϱ}$. It is shown that $T^{k}_{ϱ}$ is strongly Morita equivalent to $A_{ϱ}$, and that $T_{ϱ}^{k} ⊗ M_{p^{∞}}$ is isomorphic to $A_{ϱ} ⊗ M_{k}(ℂ) ⊗ M_{p^{∞}}$ if and only if the set of prime factors of k is a subset of the set of prime factors of p.
LA - eng
KW - non-commutative torus; equivalence bimodule; circle algebra; real rank 0; crossed product; UHF-algebra; Cuntz algebra; fibre; strongly Morita equivalent; prime factors
UR - http://eudml.org/doc/284857
ER -