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Quantum Unique Factorisation Domains
Author(s) -
Launois S.,
Lenagan T. H.,
Rigal L.
Publication year - 2006
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610706022927
Subject(s) - noncommutative geometry , factorization , mathematics , pure mathematics , quantum , iterated function , nilpotent , lie algebra , polynomial ring , algebra over a field , polynomial , skew , discrete mathematics , physics , quantum mechanics , mathematical analysis , algorithm , astronomy
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 q (GL n ) and q (SL n ).