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THE MAXIMAL ORDER PROPERTY FOR QUANTUM DETERMINANTAL RINGS

Published online by Cambridge University Press:  10 December 2003

T. H. Lenagan  and
L. Rigal
T. H. Lenagan
Affiliation:
School of Mathematics, University of Edinburgh, James Clerk Maxwell Building, King’s Buildings, Mayfield Road, Edinburgh EH9 3JZ, UK (tom@maths.ed.ac.uk)
L. Rigal
Affiliation:
Université Jean Monnet (Saint-Étienne), Faculté des Sciences et Techniques, Département de Mathématiques, 23 rue du Docteur Paul Michelon, 42023 Saint-Étienne Cédex 2, France (Laurent.Rigal@univ-st-etienne.fr)
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Abstract

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We develop a method of reducing the size of quantum minors in the algebra of quantum matrices $\mathcal{O}_q(M_n)$. We use the method to show that the quantum determinantal factor rings of $\mathcal{O}_q(M_n)c$ are maximal orders, for $q$ an element of $\mathbb{C}$ transcendental over $\mathbb{Q}$.

AMS 2000 Mathematics subject classification: Primary 16P40; 16W35; 20G42

Keywords

quantum matricesquantum minorsquantum determinantal ringsmaximal orders
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 46 , Issue 3 , October 2003 , pp. 513 - 529
Copyright
Copyright © Edinburgh Mathematical Society 2003