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

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

2009-05-15

arxiv.org/abs/0905.2468v2

J.Phys.A43:015205,2010

Physics

High Energy Physics

High Energy Physics - Theory

21 pages. v2: published version

Scientific paper

10.1088/1751-8113/43/1/015205

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.

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