Abstract
The octonion torus (or Cayley torus) appears as a coordinate algebra of extended affine Lie algebras of type A 2 and F 4 . A generalized version of the octonion torus, called division Z n -graded alternative algebras , is classified in this paper. Using the result, we can complete the classification of division ( A 2 , Z n ) -graded Lie algebras, up to central extensions, which are a generalization of the cores of extended affine Lie algebras of type A 2 .
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