Some quantum-like Hopf algebras which remain noncommutative when \(q=1\).
type: Item
instance of: scholarly article
title: Some quantum-like Hopf algebras which remain noncommutative when \(q=1\).
zbMATH Open document ID: 1045.16020
DOI: 10.1023/A:1020221319846
author: Suemi Rodríguez-Romo
author: Earl J. Taft
published in: Letters in Mathematical Physics
publication date: 2003-03-12T00:00:00Z
review text: The authors construct a quantum group using only three of the six relations defining the standard quantum group \(\text{GL}_q(2)\). They show that the quantum determinant of the obtained quantum group is group-like but not central, i.e. it does not commute with the matrix elements of the quantum group, and so the two Hopf algebras constructed in this way are not isomorphic to the standard quantum group.
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 17B37
zbMATH DE Number: 1880347
zbMATH Keywords: Hopf algebras
zbMATH Keywords: quantum groups
zbMATH Keywords: antipodes
zbMATH Keywords: Birkhoff-Witt bases
zbMATH Keywords: irreducible monomials
zbMATH Keywords: quantum determinants
zbMATH Keywords: group-like elements
reviewed by: Salih Çelik
MaRDI profile type: Publication
full work available at URL: a:1020221319846
OpenAlex ID: W143078071
description: scientific article; zbMATH DE number 1880347