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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Prime factor algebras of the coordinate ring of quantum matrices
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by K. R. Goodearl and E. S. Letzter PDF
Proc. Amer. Math. Soc. 121 (1994), 1017-1025 Request permission

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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Additional Information
  • © Copyright 1994 American Mathematical Society
  • 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