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

Tomasz Brzezinski, Wojciech Szymanski

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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 languageEnglish
JournalJournal of Noncommutative Geometry
Volume12
Issue number1
Pages (from-to)195-215
ISSN1661-6952
DOIs
Publication statusPublished - 2018

Fingerprint

Weighted Spaces
Projective Space
C*-algebra
Lens
Continuous Function
K-group
Algebra
Graph C*-algebra
Circle Action
Lens Space
Skew Product
Cyclic group
Graph in graph theory
Labeling
Fixed point
Arbitrary

Keywords

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

Cite this

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

In: Journal of Noncommutative Geometry, Vol. 12, No. 1, 2018, p. 195-215.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

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

AU - Brzezinski, Tomasz

AU - Szymanski, Wojciech

PY - 2018

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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

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KW - Graph C∗-algebra

KW - Quantum weighted projective space

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