On Poincar\'e-Birkhoff-Witt basis of quantum general linear superalgebra

TL;DR

This paper derives detailed commutation relations for the PBW generators of the quantum superalgebra U_q(gl_{M|N}), enhancing understanding of its algebraic structure.

Contribution

It provides a comprehensive derivation of the commutation relations for PBW generators in quantum superalgebra U_q(gl_{M|N}), a novel contribution to the algebra's structural theory.

Findings

Explicit commutation relations for PBW generators derived

Enhanced understanding of quantum superalgebra structure

Foundation for further algebraic and representation-theoretic studies

Abstract

We give a detailed derivation of the commutation relations for the Poincar\'e--Birkhoff--Witt generators of the quantum superalgebra $\mathrm U_q(\mathfrak{gl}_{M|N})$.