The CC^*-algebras of quantum lens and weighted projective spaces

  • Tomasz Brzeziński

    Swansea University, UK and University of Białystok, Poland
  • Wojciech Szymański

    University of Southern Denmark, Odense, Denmark
The $C^*$-algebras of quantum lens and weighted projective spaces cover
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Abstract

It is shown that the algebra of continuous functions on the quantum 2n+12n+1-dimensional lens space C(Lq2n+1(N;m0,,mn))C(L^{2n+1}_q(N; m_0,\ldots, m_n)) is a graph CC^*-algebra, for arbitrary positive weights m0,,mnm_0,\ldots, m_n. 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 Sq2n+1S_q^{2n+1} and the cyclic group ZN\mathbb Z_N, with the labelling induced by the weights. Based on this description, the KK-groups of specific examples are computed. Furthermore, the KK-groups of the algebras of continuous functions on quantum weighted projective spaces C(WPqn(m0,,mn))C(\mathbb W\mathbb P_q^n(m_0,\ldots, m_n)), interpreted as fixed points under the circle action on C(Sq2n+1)C(S_q^{2n+1}), are computed under a mild assumption on the weights.

Cite this article

Tomasz Brzeziński, Wojciech Szymański, The CC^*-algebras of quantum lens and weighted projective spaces. J. Noncommut. Geom. 12 (2018), no. 1, pp. 195–215

DOI 10.4171/JNCG/274