Real spectra of quantum groups
type: Item
instance of: scholarly article
title: Real spectra of quantum groups
zbMATH Open document ID: 1113.17008
author: Jakob Cimprič
published in: Journal of Algebra
publication date: 2004-09-23T00:00:00Z
review text: Let \(R\) be a ring. The real spectrum of \(R\), introduced by \textit{K. H. Leung, M. Marshall} and \textit{Y. Zhang} in [J. Algebra 198, No. 2, 412--427 (1997; Zbl 0909.16027)] is by the definition the set of all orderings of \(R\). This paper describes the real spectra of quantum affine rings \(k_{\mathbf q}[x_1, \dots, x_n]\), where \(k\) is a formally real affine \(\mathbb R\)-algebra and \({\mathbf q} \in M_n(\mathbb R^+)\). The description of this real spectra is reduced to the description of the real spectra of polynomial rings. For \(k = \mathbb R\), these last description is given in turn in the paper cited above by Leung, Marshall and Zhang. The paper also gives a characterization of formal reality and semireality of quantum affine rings, quantized enveloping algebras, quantized function algebras and quantized Weyl algebras.
reviewed by: Sonia Natale
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 20G42
zbMATH DE Number: 2102479
zbMATH Keywords: quantum groups
zbMATH Keywords: real algebraic geometry
zbMATH Keywords: ordered rings
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2004.03.011
OpenAlex ID: W2110011687
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DOI: 10.1016/J.JALGEBRA.2004.03.011
description: scientific article; zbMATH DE number 2102479