Centreless Lie tori have been used by E. Neher to construct all extendedaffine Lie algebras (EALAs). In this article, we study notions of isotopes andisotopy for centreless Lie tori, and we use these notions, along with Neher'sconstruction, to show that there is a 1-1 correspondence between centreless Lietori up to isotopy and families of EALAs up to isomorphism. Also, centrelessLie tori can be coordinatized by unital algebras that are in generalnonassociative, and, for many types of centreless Lie tori, there are classicalnotions of isotopes and isotopy for the coordinate algebras. We show for thosetypes that an isotope of the Lie torus is coordinatized by an isotope of itscoordinate algebra. In writing the article, we have not assumed prior knowledgeof the theories of EALAs, Lie tori or isotopy. In fact, we hope that thisarticle will help to introduce the reader to these theories and theirinterconnections.
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