Mathematical Research Letters

Volume 27 (2020)

Number 6

Weight modules of quantum Weyl algebras

Pages: 1707 – 1753



Vyacheslav Futorny (Departmento de Matemática, Universidade de São Paulo, Brazil; and International Center for Mathematics, SUSTech, Shenzhen, China)

Laurent Rigal (Université Sorbonne Paris Nord, Villetaneuse, France)

Andrea Solotar (IMAS-CONICET y Departamento de Matemática, Universidad de Buenos Aires, Argentina)


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

The authors were supported by the MathAMSud grant ”Representations, homology and Hopf algebra”. V.F. was partially supported by the CNPq grant (304467/2017-0) and by the CNPq grant (200783/2018-1). A.S. was partially supported by PIP-CONICET 11220150100483CO and UBACyT 20020170100613BA. She is a research member of CONICET (Argentina). We would like to thank Cristian Chaparro for his help with the diagrams.

Received 4 December 2018

Accepted 12 November 2019

Published 17 February 2021