2022/08/27 by Arnaud Beauville, Beauville, Arnaud
Chemistry · Computer Science · Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Bijection #Chemistry #Coding theory and cryptography #Combinatorics #Crystal structure #Crystallography #FOS: Mathematics #Geometry #Group Theory (math.GR) #Isomorphism (crystallography) #Lattice (music) #Mathematics #Mod #Physics #Reduction (mathematics) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2208.12962
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2022/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/08
For an even lattice L , the form v --> (v.v)/2 induces a quadratic form q on the (Z/2)-vector space L/2L . For the lattices associated to some particular root systems, we show that reduction mod. 2 induces a bijection between the roots of L and the vectors of L/2L with q=1 , and an isomorphism of O(L)/<-1> onto O(L/2L).