TL;DR
This paper constructs a quantum deformation of the ISL(2,C) group using a Poisson structure derived from the classical r-matrix associated with the quantum k-Poincare algebra, contributing to quantum group theory.
Contribution
It introduces a quantum deformation of the ISL(2,C) group based on a Poisson structure from the classical r-matrix, expanding quantum group frameworks.
Findings
Derived a Poisson structure on ISL(2,C) from the classical r-matrix.
Obtained a quantum deformation of ISL(2,C) via trivial quantization.
Linked the quantum k-Poincare algebra to the quantum ISL(2,C) group.
Abstract
Abstr.: The classical r-matrix implied by the quantum k-Poincare algebra of Lukierski,Nowicki and Ruegg is used to generate a Poisson structure on the ISL(2,C) group. A quantum deformation of the ISL(2,C) group ( on the Hopf algebra level ) is obtained by a trivial quantization.
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