Weight modules of quantized Weyl algebras

2018/12/05 by Vyacheslav Futorny, Futorny, Vyacheslav, Laurent Rigal +3
Mathematics · #16D30 #16D60 #16P40 #16S32 #16S36 #17B37 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1812.02118

openalex publication_date 2018/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 quantum Weyl algebras for generic values of deformation parameters. We consider two quantum versions: one by Maltsiniotis and the other one by Akhavizadegan and Jordan.

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