New quantum deformation of \(SL(2,\mathbb{C}{})\). Hopf algebra level
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.
quantum deformation of \(SL(2,\mathbb{C})\)
scientific article; zbMATH DE number 97856