New quantum deformation of \(SL(2,\mathbb{C}{})\). Hopf algebra level
type: Item
instance of: scholarly article
title: New quantum deformation of \(SL(2,\mathbb{C}{})\). Hopf algebra level
zbMATH Open document ID: 0759.17010
DOI: 10.1016/0034-4877(91)90030-Q
published in: Reports on Mathematical Physics
publication date: 1993-01-17T00:00:00Z
review text: The author investigates a new quantum deformation of \(SL(2,\mathbb{C})\) on the level of Hopf algebra by using the Manin approach, which was first proposed by Zakrzewski. The author proves that the representation theory of the deformed group is the same as the holomorphic representation theory of \(SL(2,\mathbb{C})\). In particular, the fact that the considered quantum group does not depend on the deformation parameter shows that the deforming parameter is no longer a dimensionless quantity, and this fact is very important from the point of view of the correspondence principle. Moreover, the \(R\)-matrix is involutive, so the considered quantum group is better compatible with classical groups.
reviewed by: Ye Jiachen
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 16W30
zbMATH DE Number: 97856
zbMATH Keywords: quantum deformation of \(SL(2,\mathbb{C})\)
zbMATH Keywords: Hopf algebra
zbMATH Keywords: holomorphic representation
zbMATH Keywords: quantum group
author: Stanisław Lech Woronowicz
MaRDI profile type: Publication
cites work: Q3819193
cites work: A \(q\)-analogue of \(U(\mathfrak{gl}(N+1))\), Hecke algebra, and the Yang-Baxter equation
cites work: Q5588717
cites work: Q3998175
cites work: Quantum deformation of Lorentz group
cites work: Twisted \(\text{SU}(2)\) group. An example of a non-commutative differential calculus
cites work: Compact matrix pseudogroups
cites work: Tannaka-Krein duality for compact matrix pseudogroups. Twisted SU(N) groups
cites work: Q4286085
cites work: Quantum Lorentz group having Gauss decomposition property
full work available at URL: 0034-4877(91)90030-q
OpenAlex ID: W2034804482
description: scientific article; zbMATH DE number 97856