Derivations and automorphisms of the positive part of the two-parameter quantum group U r,s (B 3)

Abstract

We compute the derivations of the positive part of the two-parameter quantum group U r,s (B 3) and show that the Hochschild cohomology group of degree 1 of this algebra is a three-dimensional vector space over the base field C. We also compute the groups of (Hopf) algebra automorphisms of the augmented two-parameter quantized enveloping algebra Ǔ r,s ≥0(B 3).