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

Tomasz Brzezinski, Wojciech Szymanski

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Resumé

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.

OriginalsprogEngelsk
TidsskriftJournal of Noncommutative Geometry
Vol/bind12
Udgave nummer1
Sider (fra-til)195-215
ISSN1661-6952
DOI
StatusUdgivet - 2018

Fingeraftryk

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

Citer dette

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

I: Journal of Noncommutative Geometry, Bind 12, Nr. 1, 2018, s. 195-215.

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer 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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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

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