Some isomorphism invariants for Lie tori

Abstract

In this paper we study the isomorphism problem for centreless Lie tori that are fgc (finitely generated as modules over their centroid). These Lie tori play a important role in the theory of extended affine Lie algebras and of multiloop Lie algebras. We introduce four isomorphism invariants for fgc centreless Lie tori, and use them together with known structural results to investigate the classification problem for fgc centreless Lie tori up to isomorphism.

This revision contains tables of invariants for classical Lie tori. It also contains more detailed statments and proofs of the results on the isomorphism problem. Finally, a gap in the proof of the theorem in Section 7 is filled