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

Keywords

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

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