Skew Symmetric Extended Affine Lie algebras

Abstract

For any skew symmetric matrix over complex numbers, we introduce an EALA and it is called Skew Symmetric Extended Affine Lie Algebra (SSEALA). This way we get a large class of EALAs and most often they are non-isomorphic. In this paper we study irreducible integrable modules for SSEALA with finite dimensional weight spaces. We classify all such modules in the level zero case with non-degenerate skew symmetric matrix.

Appeared in JPAA, 2026. This is the final version of the published paper. The introduction is rewritten and some of the results written in a organized manner