Prime factor algebras of the coordinate ring of quantum matrices

Goodearl, K. R.; Letzter, E. S.

doi:10.1090/S0002-9939-1994-1211579-1

Prime factor algebras of the coordinate ring of quantum matrices
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by K. R. Goodearl and E. S. Letzter

Proc. Amer. Math. Soc. 121 (1994), 1017-1025

DOI: https://doi.org/10.1090/S0002-9939-1994-1211579-1

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Abstract:

It is proved that every prime factor algebra of the coordinate ring ${\mathcal {O}_q}({M_n}(k))$ of quantum $n \times n$ matrices over a field k is an integral domain (albeit not necessarily commutative) when q is not a root of unity. The same conclusion follows for the quantum groups ${\mathcal {O}_q}({\text {SL}_n}(k))$ and ${\mathcal {O}_q}({\text {GL}_n}(k))$. The proof uses a q-analog of Sigurdsson’s theorem bounding the Goldie ranks of prime factors of differential operator rings; this q-analog in turn is based on results from the authors’ recent work on q-skew polynomial rings.

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Consistent multiparameter quantisation of

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