(Hopf) Algebra Automorphisms of the Hopf algebra ${\check{U}}_{r,s}^{\ge 0}(\mathfrak{s}{l}_3)$

Abstract

In this paper, we completely determine the group of algebra automorphisms for the two-parameter Hopf algebra ${\check{U}}_{r,s}^{\ge 0}(\mathfrak{s}{l}_3)$. As a result, the group of Hopf algebra automorphisms is determined for $\V$ as well. We further characterize all the derivations of the subalgebra $U_{r,s}^{+}(\mathfrak{s}{l}_3)$, and calculate its first degree Hochschild cohomology group.