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

@article{Palmkvist2009ThreealgebrasTS,
title={Three-algebras, triple systems and 3-graded Lie superalgebras},
author={Jakob Palmkvist},
journal={Journal of Physics A},
year={2009},
volume={43},
pages={015205}
}
• Jakob Palmkvist
• Published 15 May 2009
• Mathematics, Physics
• Journal of Physics A
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.
36 Citations
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