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

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

1994-11-04

arxiv.org/abs/hep-th/9411036v1

Theor.Math.Phys. 102 (1995) 10-22; Teor.Mat.Fiz. 102N1 (1995) 17-31

Physics

High Energy Physics

High Energy Physics - Theory

16 pages, LaTeX, no figures

Scientific paper

10.1007/BF01017449

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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