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Orthogonal decomposition of some affine Lie algebras in terms of their heisenberg subalgebras
Teoretičeskaâ i matematičeskaâ fizika, Tome 102 (1995) no. 1, pp. 17-31 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the present note we suggest an affinization of a theorem by Kostrikin et. al. about the decomposition of some complex simple Lie algebras $\mathcal G$ into the algebraic sum of pairwise orthogonal Cartan subalgebras. We point out that the untwisted affine Kac–Moody algebras of types $A_{p^m-1}$ ($p$ prime, $m\geq 1$), $B_r$, $C_{2^m}$, $D_r$, $G_2$, $E_7$, $E_8$ can be decomposed into the algebraic sum of pairwise orthogonal Heisenberg subalgebras. The $A_{p^m-1}$ and $G_2$ cases are discussed in great detail. Some possible applications of such decompositions are also discussed. 
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L. A. Ferreira; D. I. Olive; M. V. Saveliev. Orthogonal decomposition of some affine Lie algebras in terms of their heisenberg subalgebras. Teoretičeskaâ i matematičeskaâ fizika, Tome 102 (1995) no. 1, pp. 17-31. http://geodesic.mathdoc.fr/item/TMF_1995_102_1_a1/

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