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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The structure of quantum spheres
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by Albert Jeu-Liang Sheu PDF
Proc. Amer. Math. Soc. 129 (2001), 3307-3311 Request permission

Abstract:

We show that the C*-algebra $C\left (\mathbb {S}_{q}^{2n+1}\right )$ of a quantum sphere $\mathbb {S}_{q}^{2n+1}$, $q>1$, consists of continuous fields $\left \{f_{t}\right \}_{t\in \mathbb {T}}$ of operators $f_{t}$ in a C*-algebra $\mathcal {A}$, which contains the algebra $\mathcal {K}$ of compact operators with $\mathcal {A}/\mathcal {K}\cong C\left ( \mathbb {S}_{q} ^{2n-1}\right )$, such that $\rho _{\ast }\left ( f_{t}\right )$ is a constant function of $t\in \mathbb {T}$, where $\rho _{\ast }:\mathcal {A}\rightarrow \mathcal {A}/\mathcal {K}$ is the quotient map and $\mathbb {T}$ is the unit circle.
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Additional Information
  • Albert Jeu-Liang Sheu
  • Affiliation: Department of Mathematics, University of Kansas, Lawrence, Kansas 66045
  • Email: sheu@falcon.cc.ukans.edu
  • Received by editor(s): March 15, 2000
  • Published electronically: April 2, 2001
  • Additional Notes: The author was partially supported by NSF Grant DMS-9623008
  • Communicated by: David R. Larson
  • © Copyright 2001 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 129 (2001), 3307-3311
  • MSC (2000): Primary 46L05; Secondary 17B37, 46L89, 47B35, 58B32, 81R50
  • DOI: https://doi.org/10.1090/S0002-9939-01-06042-7
  • MathSciNet review: 1845007