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Journal Article

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

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Palmkvist,  Jakob
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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0905.2468v1.pdf
(Preprint), 214KB

JPA43_015205.pdf
(Any fulltext), 233KB

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Citation

Palmkvist, J. (2009). Three-algebras, triple systems and 3-graded Lie superalgebras. Journal of Physics A, 43(1): 015205. doi:http://dx.doi.org/10.1088/1751-8113/43/1/015205.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-606E-C
Abstract
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.