The quantum 2-dimensional Poincare group from quantum group contraction
Philippe Zaugg
TL;DR
This paper introduces a new derivation of the quantum deformation of the 2D Euclidean Poincare group using contraction of a quantum group, providing insights into quantum group structures and their algebraic properties.
Contribution
It presents a novel derivation method for the quantum 2D Euclidean Poincare group via contraction of Fun(SO_q(3)), expanding understanding of quantum group deformations.
Findings
Derived a new quantum Poincare group from Hopf algebra contraction
Connected the quantum group to the $$-Poincare algebra
Provided duality relations between the quantum group and algebra
Abstract
A new derivation of the quantum deformation of the 2 dimensional Euclidean Poincare group (cf S. Zakrzewski) is proposed. It is based on a contraction of the Hopf algebra Fun(SO_q(3)). The deformation parameter q is sent to one, as in the construction of the -Poincare deformed algebra. The quantum group obtained is dual to that algebra.
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