Abstract
There is a notion of “non-commutative Lie algebra” called Leibniz algebra, which is characterized by the following property. The bracketing [-, z] is a derivation for the bracket operation, that is, it satisfies the Leibniz identity: \( \left[ {\left[ {x,y} \right],z} \right] = \left[ {\left[ {x,z} \right],y} \right] + \left[ {x,\left[ {y,z} \right]} \right] \) cf. [LI]. When it happens that the bracket is skew-symmetric, we get a Lie algebra since the Leibniz identity becomes equivalent to the Jacobi identity.
Keywords
- Chain Complex
- Associative Algebra
- Monoidal Category
- Tensor Category
- Leibniz Algebra
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Loday, JL. (2001). Dialgebras. In: Dialgebras and Related Operads. Lecture Notes in Mathematics, vol 1763. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45328-8_2
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