  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.
