Geodesic
Integral invariant lattices in Lie algebras of type $A_{p^m-1}$
Sbornik. Mathematics, Tome 78 (1994) no. 2, pp. 447-478 Cet article a éte moissonné depuis la source Math-Net.Ru

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Integral invariant lattices associated with the standard orthogonal decomposition of a Lie algebra of type $A_{p^m-1}$ are described up to similarity. Duality in the class of invariant lattices is studied. Even unimodular root-free lattices of dimension $p^{2m}-1$ are distinguished. 
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K. S. Abdukhalikov. Integral invariant lattices in Lie algebras of type $A_{p^m-1}$. Sbornik. Mathematics, Tome 78 (1994) no. 2, pp. 447-478. http://geodesic.mathdoc.fr/item/SM_1994_78_2_a11/

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