The K-theory of twisted multipullback quantum odd spheres and complex projective spaces

Piotr M. Hajac; Ryszard Nest; David Pask; Aidan Sims; Bartosz Zielinski

doi:10.4171/JNCG/292

The K-theory of twisted multipullback quantum odd spheres and complex projective spaces

Piotr M. Hajac, Ryszard Nest, David Pask, Aidan Sims, Bartosz Zielinski

Department of Mathematical Sciences

4 Citations (Scopus)

Abstract

We find multipullback quantum odd-dimensional spheres equipped with natural U.1/-actions that yield the multipullback quantum complex projective spaces constructed from Toeplitz cubes as noncommutative quotients. We prove that the noncommutative line bundles associated to multipullback quantum odd spheres are pairwise stably non-isomorphic, and that the K-groups of multipullback quantum complex projective spaces and odd spheres coincide with their classical counterparts.We show that theseK-groups remain the same for more general twisted versions of our quantum odd spheres and complex projective spaces.

Original language	English
Journal	Journal of Noncommutative Geometry
Volume	12
Issue number	3
Pages (from-to)	823-863
Number of pages	41
ISSN	1661-6952
DOIs	https://doi.org/10.4171/JNCG/292
Publication status	Published - 2018

Keywords

Associated noncommutative line bundle
Free action on C∗-algebras
Multipullback and higher-rank graph C∗-algebras
Noncommutative deformation.

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10.4171/JNCG/292

https://arxiv.org/pdf/1512.08816.pdfLicence: Other

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title = "The K-theory of twisted multipullback quantum odd spheres and complex projective spaces",

abstract = "We find multipullback quantum odd-dimensional spheres equipped with natural U.1/-actions that yield the multipullback quantum complex projective spaces constructed from Toeplitz cubes as noncommutative quotients. We prove that the noncommutative line bundles associated to multipullback quantum odd spheres are pairwise stably non-isomorphic, and that the K-groups of multipullback quantum complex projective spaces and odd spheres coincide with their classical counterparts.We show that theseK-groups remain the same for more general twisted versions of our quantum odd spheres and complex projective spaces.",

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T1 - The K-theory of twisted multipullback quantum odd spheres and complex projective spaces

AU - Hajac, Piotr M.

AU - Nest, Ryszard

AU - Pask, David

AU - Sims, Aidan

AU - Zielinski, Bartosz

PY - 2018

Y1 - 2018

N2 - We find multipullback quantum odd-dimensional spheres equipped with natural U.1/-actions that yield the multipullback quantum complex projective spaces constructed from Toeplitz cubes as noncommutative quotients. We prove that the noncommutative line bundles associated to multipullback quantum odd spheres are pairwise stably non-isomorphic, and that the K-groups of multipullback quantum complex projective spaces and odd spheres coincide with their classical counterparts.We show that theseK-groups remain the same for more general twisted versions of our quantum odd spheres and complex projective spaces.

AB - We find multipullback quantum odd-dimensional spheres equipped with natural U.1/-actions that yield the multipullback quantum complex projective spaces constructed from Toeplitz cubes as noncommutative quotients. We prove that the noncommutative line bundles associated to multipullback quantum odd spheres are pairwise stably non-isomorphic, and that the K-groups of multipullback quantum complex projective spaces and odd spheres coincide with their classical counterparts.We show that theseK-groups remain the same for more general twisted versions of our quantum odd spheres and complex projective spaces.

KW - Associated noncommutative line bundle

KW - Free action on C∗-algebras

KW - Multipullback and higher-rank graph C∗-algebras

KW - Noncommutative deformation.

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EP - 863

JO - Journal of Noncommutative Geometry

JF - Journal of Noncommutative Geometry

IS - 3

ER -

The K-theory of twisted multipullback quantum odd spheres and complex projective spaces

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