Weight modules of quantized Weyl algebras
Vyacheslav Futorny, Laurent Rigal, Andrea Solotar
TL;DR
This paper introduces a framework for analyzing weight modules in quantum Weyl algebras, providing classifications of simple and projective modules for two quantum versions with generic parameters.
Contribution
It develops a general method for studying weight representations and applies it to classify modules in two quantum Weyl algebra variants.
Findings
Classification of simple weight modules
Description of projective modules
Applicable to two quantum algebra versions
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Algebra and Geometry · Advanced Topics in Algebra