Classification of quasifinite modules with nonzero central charges for EALAs of type A with coordinates in quantum torus

Abstract

The author first constructs a Lie algebra \( \mathfrak{L}: = \mathfrak{L}(q,w_d ) \) from rank 3 quantum torus, which is isomorphic to the core of EALAs of type Ad−1 with coordinates in quantum torus Cqd, and then gives the necessary and sufficient conditions for the highest weight modules to be quasifinite. Finally the irreducible ℤ-graded quasifinite \( \mathfrak{L} \)-modules with nonzero central charges are classified.