The ideal–center direct-sum conjecture for the current algebra

Let $J$ be the two-sided ideal of $\mathcal A_q$ generated by $\mathcal W_0$ and $\mathcal W_1$, and let $Z(\mathcal A_q)$ denote the center. Ideal–center direct-sum conjecture. The vector-space sum

$$\mathcal A_q=J+Z(\mathcal A_q)$$

is direct.

This conjecture concerns the interaction between the ideal generated by the q-Onsager generators and the center of the current algebra. Its resolution is not given in the supplied text.