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

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 $\mathcal{G}$ 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, $m\ge 1$), $B_r,C_{2^m},D_r,G_2,E_7,E_8$ 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.

16 pages, LaTeX, no figures

References in corpus (3)

• Affine Toda Solitons and Vertex Operators
• Hirota's Solitons in the Affine and the Conformal Affine Toda Models
• On a Solitonic Specialisation for the General Solutions of Some Two-Dimensional Completely Integrable Systems

Cited by in corpus (1)

• Sylvester-t' Hooft generators of sl(n) and sl(n|n), and relations between them