Automorphisms of the two-parameter Hopf algebra $\V$

TL;DR

This paper characterizes the automorphism groups of a specific two-parameter quantum algebra, revealing that its Hopf automorphisms form a rank-two torus, thus advancing understanding of its symmetry structure.

Contribution

It explicitly determines the algebra automorphism group and proves the Hopf automorphism group is isomorphic to a rank-two torus, a novel result for this algebra.

Findings

Automorphism group of the algebra is explicitly determined.

Hopf automorphism group is isomorphic to a rank-two torus.

Provides structural insights into the symmetry of the algebra.

Abstract

We determine the group of algebra automorphisms for the two-parameter quantized enveloping algebra $\V$. As an application, we prove that the group of Hopf algebra automorphisms for $\V$ is isomorphic to a torus of rank two.