Weight modules of quantized Weyl algebras

Abstract

We develop a general framework for studying relative weight representations for certain pairs consistingof an associative algebra and a commutative subalgebra. Using these tools we describe projective and simple weightmodules for a common localisation of two quantum versions of Weyl algebras, one by Maltsiniotis and the otherone by Akhavizadegan and Jordan, for generic values of the deformation parameters.