n-ary algebras: a review with applications

@article{deAzcrraga2010naryAA,
  title={n-ary algebras: a review with applications},
  author={J. A. de Azc{\'a}rraga and Jos'e Maria P'erez Izquierdo},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2010},
  volume={43},
  pages={293001}
}
This paper reviews the properties and applications of certain n-ary generalizations of Lie algebras in a self-contained and unified way. These generalizations are algebraic structures in which the two-entry Lie bracket has been replaced by a bracket with n entries. Each type of n-ary bracket satisfies a specific characteristic identity which plays the role of the Jacobi identity for Lie algebras. Particular attention will be paid to generalized Lie algebras, which are defined by even… 

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