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Orthogonal Decomposition of Some Affine Lie Algebras in Terms of their Heisenberg Subalgebras

L. A. Ferreira·D. I. Olive·M. V. Saveliev
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Abstract

In the present note we suggest an affinization of a theorem by Kostrikin et.al. about the decomposition of some complex simple Lie algebras ${\cal G}$ 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 or\-tho\-go\-nal 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. 1994-11-04. Orthogonal Decomposition of Some Affine Lie Algebras in Terms of their Heisenberg Subalgebras. https://doi.org/10.1007/bf01017449

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