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

2016/03/14 by Brzeziński, Tomasz, Szymański, Wojciech · 1 citation
#46L87 #58B32 #58B34 #FOS: Mathematics #Operator Algebras (math.OA) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1603.04678

Abstract

It is shown that the algebra of continuous functions on the quantum 2n+1-dimensional lens space C(L²ⁿ⁺¹_q(N; m₀,…, m_n)) is a graph C^*-algebra, for arbitrary positive weights m₀,…, 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 S_q²ⁿ⁺¹ and the cyclic group ℤ_N, 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(\mathbbWP_qⁿ(m₀,…, m_n)), interpreted as fixed points under the circle action on C(S_q²ⁿ⁺¹), are computed under a mild assumption on the weights.

Cited by

• On amplified graph C*-algebras as cores of Cuntz-Krieger algebras

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