Noncommutative dynamical models with quantum symmetries
type: Item
instance of: scholarly article
title: Noncommutative dynamical models with quantum symmetries
zbMATH Open document ID: 1144.17008
author: Antoine Dutriaux
author: Dimitri Gurevich
published in: Acta Applicandae Mathematicae
publication date: 2008-09-02T00:00:00Z
review text: The authors study the \(q\)-Minkowski space algebra \(\mathcal{L}(q)\) (which is a deformation of the coordinate algebra \(\mathbb{K}[gl(n)^*]\)) and its ``sl-reduction''. Their aim is to deform some dynamical models with usual symmetries into models with quantum symmetries and to find their integrals. The authors construct a family of Verma modules over both \(\mathcal{L}(q)\) and the corresponding sl-reduction, and endow both the algebras in question and the corresponding Verma modules with a \(U_q(sl(2))\)-action. Further, the authors define some dynamical models on both \(\mathcal{L}(q)\) and the corresponding sl-reduction. In particular, they introduce a \(q\)-analogue of the Runge-Lenz vector and, finally, quantize the dynamics in space-time with a spherically symmetric metric.
reviewed by: Volodymyr Mazorchuk
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 81R12
zbMATH DE Number: 5319027
zbMATH Keywords: quantum group
zbMATH Keywords: Verma modules
zbMATH Keywords: Cayley-Hamilton identity
zbMATH Keywords: reflection equation algebra
zbMATH Keywords: \(q\)-Minkowski space algebra
MaRDI profile type: Publication
full work available at URL: s10440-008-9201-y
OpenAlex ID: W2004123085
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DOI: 10.1007/S10440-008-9201-Y
description: scientific article; zbMATH DE number 5319027