The quasitriangular Malcev isomorphism conjecture

For each $n$, let ${\mathfrak{qtr}}_n$ be the Lie algebra generated by the elements $r_{ij}$, subject to the classical Yang–Baxter relations, and let ${\mathbf{QTr}}_n$ be the group generated by the elements $R_{ij}$, subject to the quantum Yang–Baxter relations. Let ${\rm grLie}({\mathbf{QTr}}_n)$ denote the associated graded Lie algebra of the Malcev Lie algebra of ${\mathbf{QTr}}_n$ with respect to its lower central series filtration. The natural surjective homomorphism $\phi_{{\mathfrak{qtr}}_n}:{\mathfrak{qtr}}_n\to {\rm grLie}({\mathbf{QTr}}_n)$ is induced by $r_{ij}\mapsto\log R_{ij}$. Quasitriangular Malcev isomorphism conjecture. The homomorphism $\phi_{{\mathfrak{qtr}}_n}$ is an isomorphism. This is the quasitriangular case of the preceding graded-Malcev assertion; the paper proves the analogous triangular statement but leaves this map as the conjectural case.