Transitivity in integral symplectic forms

Abstract

A Symplectic lattice L is a free Z-module of finite rank endowed with a non-degenerate alternating bilinear form. Thus we have a bilinear mapping Φ of L × L into the domain of integers Z; we donote Φ (α, β) by α · β (where α, β ∈ L). Then α2 = 0 and α·β = −β·α.