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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 \(\mathbb{C}\).

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