(Hopf) Algebra Automorphisms of the Hopf algebra ${\check U}^{\geq 0}_{r,s}({\mathfrak sl_{3}})$

TL;DR

This paper fully characterizes the algebra and Hopf algebra automorphisms of a specific two-parameter quantum group related to sl3, and analyzes derivations and Hochschild cohomology of its positive part.

Contribution

It provides a complete description of automorphism groups and derivations for the two-parameter quantum group ${reve U}_{r,s}^{ ext{geq} 0}( ext{sl}_3)$, advancing understanding of its symmetries.

Findings

Automorphism group of ${reve U}_{r,s}^{ ext{geq} 0}( ext{sl}_3)$ determined

Hopf algebra automorphisms characterized for the algebra

Derivations and Hochschild cohomology of $U^{+}_{r,s}( ext{sl}_3)$ calculated

Abstract

In this paper, we completely determine the group of algebra automorphisms for the two-parameter Hopf algebra ${\check U}_{r,s}^{\geq 0}({\mathfrak sl_{3}})$. As a result, the group of Hopf algebra automorphisms is determined for $\V$ as well. We further characterize all the derivations of the subalgebra $U^{+}_{r,s}({\mathfrak sl_{3})}$, and calculate its first degree Hochschild cohomology group.