Skew Symmetric Extended Affine Lie algebras

TL;DR

This paper introduces a new class of extended affine Lie algebras derived from skew symmetric matrices and classifies their irreducible integrable modules at level zero.

Contribution

It defines Skew Symmetric Extended Affine Lie Algebras (SSEALAs) and provides a classification of their irreducible integrable modules with finite dimensional weight spaces.

Findings

Introduced SSEALAs based on skew symmetric matrices.

Classified irreducible integrable modules at level zero.

Most SSEALAs are non-isomorphic.

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.