Color Lie algebra

Summary

A color Lie algebra is an algebra graded by an abelian group $\Gamma$. Its bracket satisfies antisymmetry and the Jacobi identity up to scalar factors, given by a commutation factor on $\Gamma$. For the trivial group it is a Lie algebra, and for $\Gamma = \Z/2\Z$ with the usual signs it is a Lie superalgebra. Color Lie algebras, also called $\varepsilon$-Lie algebras, give a common frame for these two theories and allow more general gradings.