Given a semisimple Lie algebra $\mathfrak g$ with Cartan matrix $a_{ij}$, the quantum group $U_q(\mathfrak g)$ is usually defined as the $\mathbb Q(q)$-algebra with generators $K_i$, $E_i$, $F_i$ (the $K_i$ are invertible and commute with each other) and relations $$ \begin{split} K_iE_j &K_i^{-1}=q^{\langle\alpha_i,\alpha_j\rangle}E_j\qquad\qquad K_iF_j K_i^{-1}=q^{-\langle\alpha_i,\alpha_j\rangle}F_j\\;, \\\ &[E_i,F_j]=\delta_{ij}\frac{K_i-K_i^{-1}} {\quad q^{\langle\alpha_i,\alpha_i\rangle/2} -q^{-\langle\alpha_i,\alpha_i\rangle/2}\quad}\\:, \end{split} $$ along with two more complicated relations that I won't reproduce here.
One then defines the comultiplication, counit, and antipode by some more formulas.

Is there a way of defining $U_q(\mathfrak g)$ that doesn't involve writing down all those formulas?

In other words, is there a procedure that takes $\mathfrak g$ as input, produces $U_q(\mathfrak g)$ as output, and doesn't involve the choice of a Cartan subalgebra of $\mathfrak g$?

Given a semisimple Lie algebra $\mathfrak g$ with Cartan matrix $a_{ij}$, the quantum group $U_q(\mathfrak g)$ is usually defined as the $\mathbb Q(q)$-algebra with generators $K_i$, $E_i$, $F_i$ (the $K_i$ are invertible and commute with each other) and relations $$ \begin{split} K_iE_j &K_i^{-1}=q^{\langle\alpha_i,\alpha_j\rangle}E_j\qquad\qquad K_iF_j K_i^{-1}=q^{-\langle\alpha_i,\alpha_j\rangle}F_j\, \\\ &[E_i,F_j]=\delta_{ij}\frac{K_i-K_i^{-1}} {\quad q^{\langle\alpha_i,\alpha_i\rangle/2} -q^{-\langle\alpha_i,\alpha_i\rangle/2}\quad}\, \end{split} $$ along with two more complicated relations that I won't reproduce here.
One then defines the comultiplication, counit, and antipode by some more formulas.

Is there a way of defining $U_q(\mathfrak g)$ that doesn't involve writing down all those formulas?

In other words, is there a procedure that takes $\mathfrak g$ as input, produces $U_q(\mathfrak g)$ as output, and doesn't involve the choice of a Cartan subalgebra of $\mathfrak g$?