Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4593228 | Journal of Number Theory | 2016 | 22 Pages |
Abstract
The paper narrows down the possible automorphisms of extremal even unimodular lattices of dimension 72. With extensive computations in Magma[7] 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 Γ72Γ72 from [17] is the unique extremal even unimodular lattice of dimension 72 that admits a large automorphism, where a d×dd×d matrix is called large, if its minimal polynomial has an irreducible factor of degree >d/2>d/2.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Gabriele Nebe,