An even unimodular 72-dimensional lattice of minimum 8
نویسنده
چکیده
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.
منابع مشابه
Rank 72 high minimum norm lattices
Given a polarization of an even unimodular lattice and integer k ≥ 1, we define a family of unimodular lattices L(M, N, k). Of special interest are certain L(M,N, 3) of rank 72. Their minimum norms lie in {4, 6, 8}. Norms 4 and 6 do occur. Consequently, 6 becomes the highest known minimum norm for rank 72 even unimodular lattices. We discuss how norm 8 might occur for such a L(M,N, 3). We note ...
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تاریخ انتشار 2011