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Proceedings of the American Mathematical Society

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

 

 

Prime factor algebras of the coordinate ring of quantum matrices


Authors: K. R. Goodearl and E. S. Letzter
Journal: Proc. Amer. Math. Soc. 121 (1994), 1017-1025
MSC: Primary 16W30; Secondary 16S36, 17B37
DOI: https://doi.org/10.1090/S0002-9939-1994-1211579-1
MathSciNet review: 1211579
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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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DOI: https://doi.org/10.1090/S0002-9939-1994-1211579-1
Article copyright: © Copyright 1994 American Mathematical Society