Abstract
We study even unimodular Euclidean lattices in dimension 32 with small root systems. It is shown that such lattices are generated by the vectors ν with (ν, ν) ⩽ 4. For lattices without roots we obtain special properties of the configuration of minimal vectors which are reminiscent of strongly regular graphs.
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 116, pp. 44–55, 1982.
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Venkov, B.B. Even unimodular Euclidean lattices in dimension 32. J Math Sci 26, 1860–1867 (1984). https://doi.org/10.1007/BF01670570
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DOI: https://doi.org/10.1007/BF01670570