Weyl algebras for quantum homogeneous spaces
type: Item
instance of: scholarly article
title: Weyl algebras for quantum homogeneous spaces
zbMATH Open document ID: 1541.14067
author: Gail Letzter
author: Siddhartha Sahi
author: Hadi Salmasian
published in: Journal of Algebra
publication date: 2024-07-02T00:00:00Z
review text: The authors present a new family of quantum Weyl algebras associated to symmetric pairs \((\mathfrak{g},\mathfrak{k})\) of Type AI, Type AII, and the Type A diagonal case, where the polynomial part is the quantum analog of functions on homogeneous spaces corresponding to symmetric matrices, skew symmetric matrices, and the entire space of matrices of a given size. The construction uses twisted tensor products and their deformations combined with invariance properties derived from quantum symmetric pairs. These quantum Weyl algebras admit \(U_q(\mathfrak{gl}_N)\)-module algebra structures compatible with standard ones on the polynomial part, have relations that are expressed nicely via matrices, and are closely related to an algebra arising in the theory of quantum bounded symmetric domains.
reviewed by: Mee Seong Im
Mathematics Subject Classification ID: 14M15
Mathematics Subject Classification ID: 16G60
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 05E10
zbMATH DE Number: 7874682
zbMATH Keywords: Weyl algebras
zbMATH Keywords: quantum symmetric pairs
zbMATH Keywords: twisted tensor products
zbMATH Keywords: reflection equations
MaRDI profile type: Publication
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DOI: 10.1016/J.JALGEBRA.2023.12.023
description: scientific article; zbMATH DE number 7874682