Lie tori of type B2 and graded-simple Jordan structures covered by a triangle

We classify two classes of B2-graded Lie algebras which have a second compatible grading by an abelian group \Lambda: (a) \Lambda-graded-simple, \Lambda torsion-free and (b) division-\Lambda-graded. Our results describe the centreless cores of a class of affine reflection Lie algebras, hence apply in particular to the centreless cores of extended affine Lie algebras, the so-called Lie tori, for which we recover results of Allison-Gao and Faulkner. Our classification (b) extends a recent result of Benkart-Yoshii.

Both classifications are consequences of a new description of Jordan algebras covered by a triangle, which correspond to these Lie algebras via the Tits-Kantor-Koecher construction. The Jordan algebra classifications follow from our results on graded-triangulated Jordan triple systems. They generalize work of McCrimmon and the first author as well as the Osborn-McCrimmon-Capacity 2-Theorem in the ungraded case.

Erhard Neher < Erhard.Neher@uottawa.ca >

Maribel Tocón < td1tobam@uco.es >

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