Physics Maths Engineering

An explicit formula of powers of the 2 × 2 quantum matrices and its applications

Abstract

We present an explicit formula of the powers for the 2×2 quantum matrices, that is a natural quantum analogue of the powers of the usual 2 × 2 matrices. As applications, we give some non-commutative relations of the entries of the powers for the 2 × 2 quantum matrices, which is a simple proof of the results of Vokos-Zumino-Wess (1990).