The 2-Dimensional Quantum Euclidean Algebra

TL;DR

This paper constructs the algebra dual to a quantum deformation of the 2D Euclidean group, linking it to $SU_q(2)$ through contraction methods, advancing understanding of quantum group structures.

Contribution

It introduces the algebra dual to the quantum Euclidean group and connects it to $SU_q(2)$ via contraction, providing new insights into quantum algebra relationships.

Findings

Constructed the algebra dual to the quantum Euclidean group.

Derived the algebra from $SU_q(2)$ through contraction.

Established connections between quantum Euclidean algebra and $SU_q(2)$.

Abstract

The algebra dual to Woronowicz's deformation of the 2-\-di\-men\-sion\-al Euclidean group is constructed. The same algebra is obtained from $SU_{q}(2)$ via contraction on both the group and algebra levels.