Some Remarks on the Two Parameters Quantum Algebra $SU_{p,k}$}

TL;DR

This paper explores the relationships between two-parameter quantum algebra $SU_{p,k}(2)$ and the single-parameter algebra $SU_q(2)$, focusing on their algebraic structures and representations.

Contribution

It provides explicit relations between $SU_{p,k}(2)$ and $SU_q(2)$ quantities, including Casimir operators, eigenvectors, and tensor coefficients.

Findings

Relations between $SU_{p,k}(2)$ and $SU_q(2)$ quantities established

Explicit formulas for Casimir operators and eigenvectors derived

Connections between matrix elements and Clebsch-Gordan coefficients shown

Abstract

The two parameters quantum algebra $SU_{p,k}(2)$ can be obtained from a single parameter algebra $SU_q(2)$. This fact gives some relations between $SU_{p,k}(2)$ quantities and the corresponding ones of the $SU_q(2)$ algebra. In this paper are mentioned the relations concerning: Casimir operators, eigenvectors, matrix elements, Clebsch Gordan coefficients and irreducible tensors.