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Proceedings of the American Mathematical Society

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

 
 

 

The structure of quantum spheres


Author: Albert Jeu-Liang Sheu
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
Published electronically: April 2, 2001
MathSciNet review: 1845007
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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

Keywords: Quantum spheres, quantum groups, groupoid C*-algebras, Toeplitz algebras
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
Article copyright: © Copyright 2001 American Mathematical Society