On extremal even unimodular 72-dimensional lattices
نویسندگان
چکیده
منابع مشابه
On extremal even unimodular 72-dimensional lattices
By computer search we show that the lattice Γ from [9] is the unique extremal even unimodular 72-dimensional lattices that can be constructed as proposed in [6].
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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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We extend the results of Ozeki on the configurations of extremal even unimodular lattices. Specifically, we show that if L is such a lattice of rank 56, 72, or 96, then L is generated by its minimal-norm vectors. Mathematics Subject Classification (2000). 11H06 (52C07, 05B30).
متن کاملAutomorphisms of extremal unimodular lattices in dimension 72
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 a...
متن کاملAn even unimodular 72-dimensional lattice of minimum 8
An even unimodular 72-dimensional lattice Γ having minimum 8 is constructed as a tensor product of the Barnes lattice and the Leech lattice over the ring of integers in the imaginary quadratic number field with discriminant −7. The automorphism group of Γ contains the absolutely irreducible rational matrix group (PSL2(7)× SL2(25)) : 2.
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2013
ISSN: 0025-5718,1088-6842
DOI: 10.1090/s0025-5718-2013-02744-5