Noncommutative symmetric algebras of two-sided vector spaces
type: Item
instance of: scholarly article
title: Noncommutative symmetric algebras of two-sided vector spaces
zbMATH Open document ID: 1004.16022
author: Patrick, David
published in: Journal of Algebra
publication date: 2002-11-10T00:00:00Z
review text: Let \(k\) be a field, and let \(E\) be a free \(k\)-bimodule, or in other words, a two-sided \(k\)-vector space. The author introduces a concept of admissible two-sided \(k\)-vector spaces and defines for such a space a noncommutative analog of the symmetric algebra. Then he computes the skew fields of fractions for some classes of admissible two-sided vector spaces. The components of degree zero of these skew fields can be considered as function fields of noncommutative ruled surfaces (cf. [\textit{M. Artin, M. Van den Bergh}, J. Algebra 133, No. 2, 249-271 (1990; Zbl 0717.14001)]). As an application a clear description of the birational equivalence classes of certain types of such surfaces is obtained.
reviewed by: Aleksandr G. Aleksandrov
Mathematics Subject Classification ID: 16S38
Mathematics Subject Classification ID: 16S50
Mathematics Subject Classification ID: 16S10
Mathematics Subject Classification ID: 16S60
Mathematics Subject Classification ID: 14A22
Mathematics Subject Classification ID: 14J26
zbMATH DE Number: 1566951
zbMATH Keywords: noncommutative symmetric algebras
zbMATH Keywords: bimodules
zbMATH Keywords: tensor algebras
zbMATH Keywords: skew fields of frractions
zbMATH Keywords: function fields
zbMATH Keywords: noncommutative ruled surfaces
MaRDI profile type: Publication
OpenAlex ID: W2034605121
cites work: Twisted homogeneous coordinate rings
cites work: Q3997571
cites work: Q3786586
cites work: A translation principle for the four-dimensional Sklyanin algebras
DOI: 10.1006/JABR.2000.8445
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description: scientific article; zbMATH DE number 1566951