An even unimodular 72-dimensional lattice of minimum 8

Details An even unimodular 72-dimensional lattice of minimum 8 An even unimodular 72-dimensional lattice of minimum 8

2010-08-17

arxiv.org/abs/1008.2862v3

Mathematics

Number Theory

New version: Replaced Griess' offender construction by a shorter and more sophisticated description of the vectors of norm 6 t

Scientific paper

An even unimodular 72-dimensional lattice $\Gamma $ 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 $\Gamma $ contains the absolutely
irreducible rational matrix group $(\PSL_2(7) \times \SL _2(25)) : 2$.

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