The structure of quantum spheres

Sheu, Albert

doi:10.1090/S0002-9939-01-06042-7

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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