On the field of fractions of certain quantum algebras
type: Item
instance of: scholarly article
title: On the field of fractions of certain quantum algebras
zbMATH Open document ID: 0820.17015
published in: Journal of Algebra
publication date: 1995-03-26T00:00:00Z
review text: The authors show that the field of fractions of certain algebras appearing in the theory of quantum groups are isomorphic to the field of fractions of quantum \(n\)-space, when the quantum parameter \(q\) is not a root of unity. More precisely, the quantum Serre relations of type \(A_ n\) and the relations defining the quantum Weyl algebra induce \(q\)- commutation relations in the field of fractions. They also study the separation of these skew fields using standard embeddings in noncommutative series. The first part of the article studies the field of fractions of \(U_ q^ + (s\ell_ n)\), the quantum analogue of the universal enveloping algebra of the Lie algebra of strictly upper triangular matrices. The second part studies the quantum Weyl algebra as differential operators arising in quantum differential calculus.
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 16W30
zbMATH DE Number: 703029
zbMATH Keywords: field of fractions
zbMATH Keywords: quantum groups
zbMATH Keywords: quantum \(n\)-space
zbMATH Keywords: quantum Serre relations
zbMATH Keywords: quantum Weyl algebra
zbMATH Keywords: \(q\)-commutation relations
author: Jacques Alev
author: François Dumas
reviewed by: Earl J. Taft
MaRDI profile type: Publication
full work available at URL: jabr.1994.1336
OpenAlex ID: W1982074348
DOI: 10.1006/JABR.1994.1336
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description: scientific article; zbMATH DE number 703029