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

## TL;DR

This paper proves that all Cartan subalgebras are conjugate in a class of extended affine Lie algebras with a specific type of centreless core, resolving a long-standing open problem in the field.

## Contribution

It establishes the conjugacy of Cartan subalgebras for EALAs with a non-fgc centreless core of type A, completing the conjugacy classification.

## Key findings

- Proves conjugacy of Cartan subalgebras in the specified class of EALAs.
- Completes the conjugacy problem for all EALAs.
- Addresses the last open case in the classification of Cartan subalgebras.

## Abstract

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