The quasitriangular group cohomology isomorphism conjecture

For each $n$, let $QA_n$ be the quadratic algebra generated by the cohomology classes associated with the generators of the quasitriangular group, and let $\eta_n:QA_n\to H^*({\mathbf{QTr}}_n,\mathbb{Q})$ be the natural homomorphism obtained by pulling back the standard degree-one generators along the projections ${\mathbf{QTr}}_n\to{\mathbf{QTr}}_2$. Quasitriangular cohomology isomorphism conjecture. The homomorphism

$$\eta_n:QA_n\to H^*({\mathbf{QTr}}_n,\mathbb{Q})$$

is an isomorphism. The analogous map $\xi_n$ for the triangular groups is proved to be an isomorphism, and the source explains that this result would follow from the quasitriangular Malcev isomorphism conjecture.