In mathematics, a Zinbiel algebra or dual Leibniz algebra is a module over a commutative ring with a bilinear product satisfying the defining identity: Zinbiel algebras were introduced by Jean-Louis Loday (1995).
The name was proposed by Jean-Michel Lemaire as being "opposite" to Leibniz algebra.
[1] In any Zinbiel algebra, the symmetrised product is associative.
A Zinbiel algebra is the Koszul dual concept to a Leibniz algebra.
The free Zinbiel algebra over V is the tensor algebra with product where the sum is over all