2014/09/30 by Gabriele Nebe, Nebe, Gabriele
Mathematics · #11H56 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11H56
paper · pdf · doi:10.48550/arxiv.1409.8473
arxiv created 2014/09/30 · arxiv updated 2014/10/01
The paper narrows down the possible automorphisms of extremal even unimodular lattices of dimension 72. With extensive computations in \sc Magma using the very sophisticated algorithm for computing class groups of algebraic number fields written by Steve Donnelly it is shown that the extremal even unimodular lattice Γ72 from \citedim72 is the unique extremal even unimodular lattice of dimension 72 that admits a large automorphism, where a d× d matrix is called large, if its minimal polynomial has an irreducible factor of degree > d/2.