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Extended affine Lie algebras. (English) Zbl 1072.17012
Let $$E$$ be an extended affine Lie algebra (EALA). The core of $$E$$ is the ideal generated by the root spaces associated to the nonisotropic roots. The main results of this paper are first, that the core of $$E$$ is a Lie torus, and second, a construction by which an EALA can be obtained from any centerless Lie torus. The author also shows that all EALAs can be obtained in this fashion. The author works with a slightly more general definition of EALA than usual, in order to obtain results for arbitrary fields of characteristic; he shows that adding a discreteness condition recovers the usual definition for (tame) EALAs over $$\mathbb{C}$$.

##### MSC:
 17B65 Infinite-dimensional Lie (super)algebras 17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras 17B70 Graded Lie (super)algebras