We show the existence of a nonzero graded form on a Lie torus by the existence of a nonzero graded form on a structurable torus. This gives a simple characterization of the core of an extended aﬃne Lie algebra (EALA). Namely, the core of any EALA is a Lie torus, and any centreless Lie torus is the centreless core of some EALA. We also show that a graded form on a Lie torus is unique up to scalars.
Cite this article
Yoji Yoshii, Lie Tori—A Simple Characterization of Extended Aﬃne Lie Algebras. Publ. Res. Inst. Math. Sci. 42 (2006), no. 3, pp. 739–762