Quantum unique factorisation domains

Launois, Stephane and Lenagan, T.H. and Rigal, L. (2006) Quantum unique factorisation domains. Journal of the London Mathematical Society, 74 (2). pp. 321-340. ISSN 0024-6107. (Full text available)

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http://dx.doi.org/10.1112/S0024610706022927

Abstract

We prove a general theorem showing that iterated skew polynomial extensions of the type that fit the conditions needed by Cauchon's deleting derivations theory and by the Goodearl-Letzter stratification theory are unique factorisation rings in the sense of Chatters and Jordan. This general result applies to many quantum algebras; in particular, generic quantum matrices and quantized enveloping algebras of the nilpotent part of a semisimple Lie algebra are unique factorisation domains in the sense of Chatters. The result also extends to generic quantum grassmannians (by using noncommutative dehomogenisation) and to the quantum groups O-q (GL(n)) and O-q (SLn).

Item Type: Article
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science
Depositing User: Stephane Launois
Date Deposited: 06 Sep 2008 16:44
Last Modified: 28 May 2014 10:56
Resource URI: http://kar.kent.ac.uk/id/eprint/7411 (The current URI for this page, for reference purposes)
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