Non-commutative Moore sequence conjecture for idèle class groups

Let $A$ be a finite-dimensional simple $\mathbb{Q}$-algebra with center $F$.

Non-commutative Moore sequence conjecture. One expects an isomorphism

$$K_{2}(\mathsf{LCA}_{A})\cong K_{2}(\mathsf{LCA}_{F}).$$

This conjecture proposes that the relevant $K_{2}$-group for a simple non-commutative algebra reduces to the corresponding commutative case, extending the analogy with Moore's formulation of Hilbert reciprocity. Its relationship with the Merkurjev–Suslin conjecture is discussed in the source, and the claim remains open.