Simple lattices and free algebras of modular forms

We study the algebras of modular forms on type IV symmetric domains for simple lattices; that is, lattices which every Heegner divisor occurs as a Borcherds product. For lattice L signature (n,2) with 3≤n≤10, we prove graded algebra maximal reflection subgroup orthogonal group is freely generated. also show that, five exceptions, discriminant kernel