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We construct a Lie algebra L from rank 3 quantum tori and show that it is isomorphic to the core of extended affine Lie algebras of type A 1 . Then we construct two classes - which turn out to be exhaustive - of irreducible ℤ-graded highest weight L-modules and give necessary and sufficient conditions for these modules to have finite-dimensional homogeneous subspaces. As a consequence, we also determine all the irreducible ℤ-graded L-modules with nonzero center and finite-dimensional homogeneous subspaces.

Modules for the core of extended affine Lie algebras of typeA1with coordinates in rank 2 quantum tori

Modules for the core of extended affine Lie algebras of typeA₁with coordinates in rank 2 quantum tori