春雨里 - 吴青峰, 李宇春

In this paper we consider all these nonassociative algebras defined by the action of invariant subspaces of the symmetric group $Σ_3$ on the associator of the considered laws.

This is the final paper in a series of four, concerning the surface $T \times T$ embedded in $\mathbb{CP}^8$, where $T$ is a the one dimensional torus. In this paper we compute the fundamental group of the Galois cover of the surface with respect to a generic projection onto $\mathbb{CP}^2$, and show that it is nilpotent of class 3. This is the first time such a group is presented as the fundamental group of a Galois cover of a surface.