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. 
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