Geodesic
Integral invariant lattices in Lie algebras of type $A_{p^m-1}$
Sbornik. Mathematics, Tome 78 (1994) no. 2, pp. 447-478

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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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     author = {K. S. Abdukhalikov},
     title = {Integral invariant lattices in {Lie} algebras of type $A_{p^m-1}$},
     journal = {Sbornik. Mathematics},
     pages = {447--478},
     publisher = {mathdoc},
     volume = {78},
     number = {2},
     year = {1994},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1994_78_2_a11/}
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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/