Matrix-element bialgebras determined by quadratic coordinate algebras
type: Item
instance of: scholarly article
title: Matrix-element bialgebras determined by quadratic coordinate algebras
zbMATH Open document ID: 0791.17015
published in: Journal of Algebra
publication date: 1994-01-03T00:00:00Z
review text: Some properties of nonstandard quantum deformations of \(GL(n)\) are difficult to establish or require very lengthy calculations. If the nonstandard deformation is related to a standard one via a twisting operation one can reduce the problem to the case of one-parameter deformations. In this paper the author provides a more systematic approach to general quantum deformations which promises to facilitate the establishing of certain properties of these Hopf algebras, such as polynomiality or the existence of the antipode. The method is based on a construction of Manin. The author uses this method in certain special cases such as the \(N\)-parameter deformation of \(GL(n)\) and some quantum groups arising from two-dimensional coordinate algebras.
reviewed by: Stefano Capparelli
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 16W30
zbMATH DE Number: 480477
zbMATH Keywords: \(N\)-parameter deformation of \(GL(n)\)
zbMATH Keywords: quantum deformations
zbMATH Keywords: Hopf algebras
zbMATH Keywords: polynomiality
zbMATH Keywords: antipode
zbMATH Keywords: quantum groups
zbMATH Keywords: two-dimensional coordinate algebras
author: Anthony Sudbery
MaRDI profile type: Publication
full work available at URL: jabr.1993.1137
OpenAlex ID: W1974994993
DOI: 10.1006/JABR.1993.1137
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description: scientific article; zbMATH DE number 480477