The quantum determinant of the elliptic algebra $\mathcal{A}_{q,p}(\mathfrak{\widehat{gl}}_N)$

TL;DR

This paper introduces the quantum determinant for the elliptic quantum algebra _{q,p}() and proves it generates the algebra's center, advancing understanding of elliptic quantum groups.

Contribution

The paper defines the quantum determinant for _{q,p}() and proves its centrality.

Findings

Quantum determinant generates the center of _{q,p}()

Establishes foundational property of elliptic quantum algebra

Advances algebraic understanding of elliptic quantum groups

Abstract

We introduce the quantum determinant for the elliptic quantum algebra $\mathcal{A}_{q,p}(\mathfrak{\widehat{gl}}_N)$ and prove that it generates the center of this algebra.