Jacobi-type identities in algebras and superalgebras

@article{Lavrov2014JacobitypeII,
  title={Jacobi-type identities in algebras and superalgebras},
  author={Peter M. Lavrov and Ol'ga Vasil'evna Radchenko and Igor Viktorovich Tyutin},
  journal={Theoretical and Mathematical Physics},
  year={2014},
  volume={179},
  pages={550-558}
}
We introduce two remarkable identities written in terms of single commutators and anticommutators for any three elements of an arbitrary associative algebra. One is a consequence of the other (fundamental identity). From the fundamental identity, we derive a set of four identities (one of which is the Jacobi identity) represented in terms of double commutators and anticommutators. We establish that two of the four identities are independent and show that if the fundamental identity holds for an… 

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