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Three-algebras, triple systems and 3-graded Lie superalgebras

par Palmkvist, Jakob
Référence International journal of modern physics A, 43, page (015205)
Publication Publié, 2009

Article révisé par les pairs

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Résumé :

The three-algebras used by Bagger and Lambert in N = 6 theories of ABJM type are in one-to-one correspondence with a certain type of Lie superalgebras. We show that the description of three-algebras as generalized Jordan triple systems naturally leads to this correspondence. Furthermore, we show that simple three-algebras correspond to simple Lie superalgebras, and vice versa. This gives a classification of simple three-algebras from the well-known classification of simple Lie superalgebras. © 2010 IOP Publishing Ltd.