Jordan tori for a torsion free abelian group

Abstract

We classify Jordan G-tori, where G is any torsion-free abelian group. Using the Zelmanov prime structure theorem, such a class divides into three types, the Hermitian type, the Clifford type, and the Albert type. We concretely describe Jordan G-tori of each type.

Keywords

Jordan tori / extended affine Lie algebra / invariant affine reflection algebra

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Higher Education Press and Springer-Verlag Berlin Heidelberg