INVARIANT LATTICES, THE LEECH LATTICE AND ITS EVEN UNIMODULAR ANALOGUES IN THE LIE ALGEBRAS $ A_{p-1}$

For any prime 2$ SRC=http://ej.iop.org/images/0025-5734/58/2/A09/tex_sm_3113_img2.gif/> a classification (up to similarity) is given of all invariant integral lattices that correspond to an orthogonal decomposition of the Lie algebra . Even unimodular lattices without roots are distinguished. For they contain the Leech lattice. For some of the resulting lattices the automorphism groups are studied, and lower bounds for the minimal length of vectors are obtained.Figures: 2. Bibliography: 17 titles.