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

Research output: Contribution to journal › Journal article › Research › peer-review

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The K-theory of twisted multipullback quantum odd spheres and complex projective spaces. / Hajac, Piotr M.; Nest, Ryszard; Pask, David; Sims, Aidan; Zielinski, Bartosz.

In: Journal of Noncommutative Geometry, Vol. 12, No. 3, 2018, p. 823-863.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Hajac, PM, Nest, R, Pask, D, Sims, A & Zielinski, B 2018, 'The K-theory of twisted multipullback quantum odd spheres and complex projective spaces', Journal of Noncommutative Geometry, vol. 12, no. 3, pp. 823-863. https://doi.org/10.4171/JNCG/292

APA

Hajac, P. M., Nest, R., Pask, D., Sims, A., & Zielinski, B. (2018). The K-theory of twisted multipullback quantum odd spheres and complex projective spaces. Journal of Noncommutative Geometry, 12(3), 823-863. https://doi.org/10.4171/JNCG/292

Vancouver

Hajac PM, Nest R, Pask D, Sims A, Zielinski B. The K-theory of twisted multipullback quantum odd spheres and complex projective spaces. Journal of Noncommutative Geometry. 2018;12(3):823-863. https://doi.org/10.4171/JNCG/292

Author

Hajac, Piotr M. ; Nest, Ryszard ; Pask, David ; Sims, Aidan ; Zielinski, Bartosz. / The K-theory of twisted multipullback quantum odd spheres and complex projective spaces. In: Journal of Noncommutative Geometry. 2018 ; Vol. 12, No. 3. pp. 823-863.

Bibtex

@article{efd2dd6f9cec4a73b79ab1a45cbcb241,
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.",
keywords = "Associated noncommutative line bundle, Free action on C∗-algebras, Multipullback and higher-rank graph C∗-algebras, Noncommutative deformation.",
author = "Hajac, {Piotr M.} and Ryszard Nest and David Pask and Aidan Sims and Bartosz Zielinski",
year = "2018",
doi = "10.4171/JNCG/292",
language = "English",
volume = "12",
pages = "823--863",
journal = "Journal of Noncommutative Geometry",
issn = "1661-6952",
publisher = "European Mathematical Society Publishing House",
number = "3",

}

RIS

TY - JOUR

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.

UR - http://www.scopus.com/inward/record.url?scp=85056347057&partnerID=8YFLogxK

U2 - 10.4171/JNCG/292

DO - 10.4171/JNCG/292

M3 - Journal article

AN - SCOPUS:85056347057

VL - 12

SP - 823

EP - 863

JO - Journal of Noncommutative Geometry

JF - Journal of Noncommutative Geometry

SN - 1661-6952

IS - 3

ER -

ID: 215083744