Quantum unique factorisation domains

Launois, S; Lenagan, T H; Rigal, L

Quantum unique factorisation domains

Authors

Launois, S

Lenagan, T H

Rigal, L

Description

We prove a general theorem showing that iterated skew polynomial extensions of the type which 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. By using noncommutative dehomogenisation, the result also extends to generic quantum grassmannians.
25 pages