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Let ${\mathfrak g}$ be a finite dimensional complex simple Lie algebra, andlet $r,s\in \mathbb{C}^{\ast}$ be transcendental over $\mathbb{Q}$ such that$r^{m}s^{n}=1$ implies $m=n=0$. We will obtain some basic properties of thetwo-parameter quantized enveloping algebra $U_{r,s}^{+}(\mathfrak g)$. Inparticular, we will verify that the algebra $U_{r,s}^{+}(\mathfrak g)$satisfies many nice properties such as having normal separation, catenarity andDixmier-Moeglin equivalence. We shall study a concrete example, the algebra$U_{r,s}^{+}(B_{2})$ in detail. We will first determine the normal elements,prime ideals and primitive ideals for the algebra $U_{r,s}^{+}(B_{2})$, andstudy their stratifications. Then we will prove that the algebra automorphismgroup of the algebra $U_{r,s}^{+}(B_{2})$ is isomorphic to$(\mathbb{C}^{\ast})^{2}$.

The Prime ideal Stratification and The Automorphism Group of $U^{+}_{r,s}(B_{2})$