Quantum 𝑛-space as a quotient of classical 𝑛-space

Goodearl, K.; Letzter, E.

doi:10.1090/S0002-9947-00-02639-8

Quantum $n$-space as a quotient of classical $n$-space
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by K. R. Goodearl and E. S. Letzter

Trans. Amer. Math. Soc. 352 (2000), 5855-5876

DOI: https://doi.org/10.1090/S0002-9947-00-02639-8

Published electronically: August 8, 2000

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Abstract:

The prime and primitive spectra of $\mathcal {O}_{\mathbf q}(k^{n})$, the multiparameter quantized coordinate ring of affine $n$-space over an algebraically closed field $k$, are shown to be topological quotients of the corresponding classical spectra, $\operatorname {spec} \mathcal {O}(k^{n})$ and $\max \mathcal {O}(k^{n})\approx k^{n}$, provided the multiplicative group generated by the entries of $\mathbf {q}$ avoids $-1$.

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