Jacobi identity
The Jacobi identity is the name for the following equation:
[X,[Y,Z]]+[Y,[Z,X]]+[Z,[X,Y]]=0 for all X,Y,Z.
Lie algebras are the primary example of an algebra which satisfies the Jacobi identity. But note that an algebra can satisfy the Jacobi identity but yet not be anticommutative.
See also: Super Jacobi identity.
Referenced By
Algebra over a commutative ring | Algebra over a field | C. G. J. Jacobi | Carl Gustav Jacobi | Carl Gustav Jakob Jacobi | Cross product | Jakob Jacobi | Karl Gustav Jacobi | Linear associative algebra | List of Lie group topics | List of abstract algebra topics | List of mathematical topics (J-L) | Poisson bracket | Repesentation of a Lie algebra | Representation of Lie algebras | Representation of a Lie algebra | Vector cross product | Vector product
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