*-orderings and *-valuations on algebras of finite Gelfand-Kirillov dimension.
type: Item
instance of: scholarly article
title: *-orderings and *-valuations on algebras of finite Gelfand-Kirillov dimension.
zbMATH Open document ID: 1052.16021
DOI: 10.1016/S0022-4049(02)00330-4
author: Murray Marshall
published in: Journal of Pure and Applied Algebra
publication date: 2003-04-28T00:00:00Z
review text: The paper studies the real *-spectrum of a finitely generated algebra with involution over \(\mathbb{C}\) of finite Gelfand-Kirillov dimension. It is shown that for such an algebra the stability indices associated to the real *-spectrum are bounded by the Gelfand-Kirillov dimension, as in the commutative case. Birkhoff-Witt algebras of finite dimensional Lie algebras with involution are examples of such algebras. The real *-spectrum of a Birkhoff-Witt algebra is examined in detail in the 2-dimensional case. The paper is motivated by works on relationships between *-orderings, *-valuations and the reduced theory of Hermitian forms over a skewfield with involution. See also \textit{M. Marshall} [Commun. Algebra 28, No. 3, 1157-1173 (2000; Zbl 0955.16029)].
Mathematics Subject Classification ID: 16W10
Mathematics Subject Classification ID: 16W60
Mathematics Subject Classification ID: 12E15
Mathematics Subject Classification ID: 16S30
Mathematics Subject Classification ID: 16P10
Mathematics Subject Classification ID: 16P90
zbMATH DE Number: 1901786
zbMATH Keywords: growth
zbMATH Keywords: Gelfand-Kirillov dimension
zbMATH Keywords: rings with involution
zbMATH Keywords: real spectra
zbMATH Keywords: finitely generated algebras
reviewed by: Victor Petrogradsky
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1901786