### Abstract

It is shown that the algebra of continuous functions on the quantum 2nC1-dimensional lens space C(L2n+1q (N;m
_{0},...mn)) is a graph C∗-algebra, for arbitrary positive weights m
_{0},...mn. The form of the corresponding graph is determined from the skew product of the graph which defines the algebra of continuous functions on the quantum sphere S2nC1 q and the cyclic group ZN, with the labelling induced by the weights. Based on this description, the K-groups of specific examples are computed. Furthermore, the K-groups of the algebras of continuous functions on quantum weighted projective spaces C(WPn q (mm
_{0},...mn)), interpreted as fixed points under the circle action on C(S2nC1q), are computed under a mild assumption on the weights.

Original language | English |
---|---|

Journal | Journal of Noncommutative Geometry |

Volume | 12 |

Issue number | 1 |

Pages (from-to) | 195-215 |

ISSN | 1661-6952 |

DOIs | |

Publication status | Published - 2018 |

### Fingerprint

### Keywords

- quantum lens space
- quantum weighted projective space
- graph C*-algebra
- Quantum lens space
- Graph C∗-algebra
- Quantum weighted projective space

### Cite this

*Journal of Noncommutative Geometry*,

*12*(1), 195-215. https://doi.org/10.4171/JNCG/274

}

*Journal of Noncommutative Geometry*, vol. 12, no. 1, pp. 195-215. https://doi.org/10.4171/JNCG/274

**The C*-algebras of quantum lens and weighted projective spaces.** / Brzezinski, Tomasz; Szymanski, Wojciech.

Research output: Contribution to journal › Journal article › Research › peer-review

TY - JOUR

T1 - The C*-algebras of quantum lens and weighted projective spaces

AU - Brzezinski, Tomasz

AU - Szymanski, Wojciech

PY - 2018

Y1 - 2018

N2 - It is shown that the algebra of continuous functions on the quantum 2nC1-dimensional lens space C(L2n+1q (N;m 0,...mn)) is a graph C∗-algebra, for arbitrary positive weights m 0,...mn. The form of the corresponding graph is determined from the skew product of the graph which defines the algebra of continuous functions on the quantum sphere S2nC1 q and the cyclic group ZN, with the labelling induced by the weights. Based on this description, the K-groups of specific examples are computed. Furthermore, the K-groups of the algebras of continuous functions on quantum weighted projective spaces C(WPn q (mm 0,...mn)), interpreted as fixed points under the circle action on C(S2nC1q), are computed under a mild assumption on the weights.

AB - It is shown that the algebra of continuous functions on the quantum 2nC1-dimensional lens space C(L2n+1q (N;m 0,...mn)) is a graph C∗-algebra, for arbitrary positive weights m 0,...mn. The form of the corresponding graph is determined from the skew product of the graph which defines the algebra of continuous functions on the quantum sphere S2nC1 q and the cyclic group ZN, with the labelling induced by the weights. Based on this description, the K-groups of specific examples are computed. Furthermore, the K-groups of the algebras of continuous functions on quantum weighted projective spaces C(WPn q (mm 0,...mn)), interpreted as fixed points under the circle action on C(S2nC1q), are computed under a mild assumption on the weights.

KW - quantum lens space

KW - quantum weighted projective space

KW - graph C-algebra

KW - Quantum lens space

KW - Graph C∗-algebra

KW - Quantum weighted projective space

U2 - 10.4171/JNCG/274

DO - 10.4171/JNCG/274

M3 - Journal article

VL - 12

SP - 195

EP - 215

JO - Journal of Noncommutative Geometry

JF - Journal of Noncommutative Geometry

SN - 1661-6952

IS - 1

ER -