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GENERALISED QUANTUM DETERMINANTAL RINGS ARE MAXIMAL ORDERS

Part of: Lie algebras and Lie superalgebras Rings and algebras arising under various constructions Hopf algebras, quantum groups and related topics Chain conditions, growth conditions, and other forms of finiteness Linear algebraic groups and related topics

Published online by Cambridge University Press:  04 August 2020

T. H. LENAGAN  and
L. RIGAL
T. H. LENAGAN
Affiliation:
Maxwell Institute, School of Mathematics, University of Edinburgh, James Clerk Maxwell Building, The King’s Buildings, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, UK, e-mail: tom@maths.ed.ac.uk
L. RIGAL
Affiliation:
Université Sorbonne Paris Nord, LAGA, CNRS, UMR 7539, F-93430, Villetaneuse, France, e-mail: rigal@math.univ-paris13.fr
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Abstract

Generalised quantum determinantal rings are the analogue in quantum matrices of Schubert varieties. Maximal orders are the noncommutative version of integrally closed rings. In this paper, we show that generalised quantum determinantal rings are maximal orders. The cornerstone of the proof is a description of generalised quantum determinantal rings, up to a localisation, as skew polynomial extensions.

MSC classification

Primary: 16T20: Ring-theoretic aspects of quantum groups
Secondary: 16P40: Noetherian rings and modules 16S38: Rings arising from non-commutative algebraic geometry 17B37: Quantum groups (quantized enveloping algebras) and related deformations 20G42: Quantum groups (quantized function algebras) and their representations
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 63 , Issue 3 , September 2021 , pp. 515 - 525
Copyright
© The Author(s), 2020. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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