Quantum unique factorisation domains

Details Quantum unique factorisation domains Quantum unique factorisation domains

2005-01-31

arxiv.org/abs/math/0501545v1

Mathematics

Quantum Algebra

25 pages

Scientific paper

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.

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