The root system and the core of an extended affine Lie algebra
An extended affine Lie algebra (EALA) is a complex Lie
algebra which has an invariant nondegenerate form and a finite
dimensional abelian ad-diagonalizable subalgebra which satisfies
certain natural axioms. These Lie algebras were first introduced by
Hoegh-Krohn and Torresani in 1990. As examples, finite dimensional
simple Lie algebras, affine Kac-Moody Lie algebras and toroidal Lie
algebras are EALA's. There are many other examples which have been
constructed in the last few years. Given an EALA L, one can associate
to L two basic objects: the root system R of L and the Lie algebra K,
where K is the quotient of the core of L by its centre. In this paper,
we give a complete description of R and K for EALA's of non-simply laced
reduced type. The methods include a study of the graded
associative, alternative and Jordan algebras which serve as coordinate
algebras for the Lie algebra K.
B.N. Allison <bruce.allison@ualberta.ca>
Y. Gao <gao-yun@math.yale.edu>