Abstract: Generalised down-up algebras are infinite-dimensional algebras which have been extensively studied from the point of view of representation theory, as they bear several common features with enveloping algebras of Lie algebras.
We study these algebras from the point of view of non-commutative algebraic geometry, namely, we provide a complete classification of those generalised down-up algebras which are (non-commutative) Noetherian unique factorisation rings (resp. domains), as defined by Chatters and Jordan in the mid 80's.
(Joint work with S. Launois.) |