R-matrix Approach to Quantum Superalgebras su_{q}(m|n)

TL;DR

This paper explores the structure of quantum superalgebras su_q(m|n) using R-matrix formalism, providing explicit parametrizations and discussing the necessary extensions for certain cases.

Contribution

It introduces explicit parametrizations of L-matrices for su_q(m|n) and discusses the extension needed for the non-simple superalgebra su(n|n).

Findings

Explicit parametrization of L^{(+)} and L^{(-)} matrices.

Quantum deformation of su(n|n) requires extension to u(n|n).

Framework established within R-matrix formalism.

Abstract

Quantum superalgebras $su_{q}(m\mid n)$ are studied in the framework of $R$-matrix formalism. Explicit parametrization of $L^{(+)}$ and $L^{(-)}$ matrices in terms of $su_{q}(m\mid n)$ generators are presented. We also show that quantum deformation of nonsimple superalgebra $su(n\mid n)$ requires its extension to $u(n\mid n)$.