A characterization of root lattices
A vector \(r\) of a lattice \(L\) is called relevant iff for every \(p\in L\setminus \{0\}\) the inequality \((p,p)> (p,r)\) holds. The authors prove that root lattices are exactly those lattices in which the set of minimal vectors equals the set of relevant vectors.
scientific article; zbMATH DE number 1018495