Non-degenerate para-complex structures in 6D with large symmetry groups

For an almost product structure J on a manifold M of dimension 6 with non-degenerate Nijenhuis tensor , we show that the automorphism group has dimension at most 14. In the case of equality G is the exceptional Lie group . The next possible symmetry dimension is proved to be equal to 10, and G has Lie algebra . Both maximal and submaximal symmetric structures are globally homogeneous and strictly nearly para-Kahler. We also demonstrate that whenever the symmetry dimension is at least 9, then the automorphism algebra acts locally transitively.