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 >