Automorphisms of extremal unimodular lattices in dimension 72
نویسنده
چکیده
The paper narrows down the possible automorphisms of extremal even unimodular lattices of dimension 72. With extensive computations in 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 [17] 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.
منابع مشابه
On automorphisms of extremal even unimodular lattices
The automorphism groups of the three known extremal even unimodular lattices of dimension 48 and the one of dimension 72 are determined using the classification of finite simple groups. Restrictions on the possible automorphisms of 48-dimensional extremal lattices are obtained. We classify all extremal lattices of dimension 48 having an automorphism of order m with φ(m) > 24. In particular the ...
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