Lie tori of type B_2 and graded-simple Jordan structures covered by a triangle
| Autor: | Neher, Erhard, Tocón, Maribel |
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| Rok vydání: | 2011 |
| Předmět: | |
| Zdroj: | Journal of Algebra 344 (2011), 78-113 |
| Druh dokumentu: | Working Paper |
| Popis: | We classify two classes of B_2-graded Lie algebras which have a second compatible grading by an abelian group A: (a) graded-simple Lie algebras for A torsion-free and (b) division-A-graded Lie algebras. 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. Comment: 45 pages; to appear in J. Algebra |
| Databáze: | arXiv |
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