Properties of $2\times 2$ h-deformed quantum (super)matrices

TL;DR

This paper explores the properties of $2\times 2$ h-deformed quantum (super)matrices, demonstrating that their powers retain a similar structure with scaled deformation parameters through a contraction method.

Contribution

It introduces a contraction procedure showing that the $n$-th power of an $h$-deformed quantum (super)matrix is also a quantum (super)matrix with deformation parameter $nh$.

Findings

The $n$-th power of the $h$-deformed quantum (super)matrix is a quantum (super)matrix with deformation parameter $nh$.

The contraction method effectively analyzes the algebraic structure of deformed quantum matrices.

The study extends understanding of deformation parameters in quantum (super)groups.

Abstract

We investigate the $h$-deformed quantum (super)group of $2\times 2$ matrices and use a kind of contraction procedure to prove that the $n$-th power of this deformed quantum (super)matrix is quantum (super)matrix with the deformation parameter $nh$.