Conjugacy of Cartan subalgebras in EALAs with a non-fgc centreless core

We establish the conjugacy of Cartan subalgebras for extended affine Lie algebras whose centreless core is “of type A”, i. e., $\ell \times \ell$-matrices over a quantum torus $\mathcal{Q}$ whose trace lies in the commutator space of $\mathcal{Q}$. This settles the last outstanding part of the conjugacy problem for Extended Affine Lie Algebras that remained open.