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Quantum unique factorisation domains

S Launois·T H Lenagan·L Rigal
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Abstract

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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S Launois, T H Lenagan, L Rigal. 2005-01-31. Quantum unique factorisation domains. https://arxiv.org/abs/math/0501545

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