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Journal of the London Mathematical Society 2006 74(2):321-340; doi:10.1112/S0024610706022927
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© The London Mathematical Society 2006

QUANTUM UNIQUE FACTORISATION DOMAINS

S. Launois, T. H. Lenagan and L. Rigal

Laboratoire de Mathématiques – UMR6056, Université de Reims Moulin de la Housse, BP 1039, 51687 Reims cedex 2, France stephane.launois{at}univ-reims.fr
School of Mathematics, University of Edinburgh James Clerk Maxwell Building, King's Buildings, Mayfield Road, Edinburgh EH9 3JZ, United Kingdom tom{at}maths.ed.ac.uk
Université Jean Monnet (Saint-Étienne) Faculté des Sciences et Techniques, Département de Mathématiques, 23 rue du Docteur Paul Michelon, 42023 Saint-Étienne cedex 2, France laurent.rigal{at}univ-st-etienne.fr

Received 15 March 2005.

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 Oq (GLn) and Oq (SLn).


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S. Launois and T. H. Lenagan
Quantised coordinate rings of semisimple groups are unique factorisation domains
Bull. London Math. Soc., May 4, 2007; (2007) bdm025v1.
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