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
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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.
@article{TMF_1995_102_1_a1,
author = {L. A. Ferreira and D. I. Olive and M. V. Saveliev},
title = {Orthogonal decomposition of some affine {Lie} algebras in terms of their heisenberg subalgebras},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {17--31},
publisher = {mathdoc},
volume = {102},
number = {1},
year = {1995},
language = {en},
url = {http://geodesic.mathdoc.fr/item/TMF_1995_102_1_a1/}
}
TY - JOUR AU - L. A. Ferreira AU - D. I. Olive AU - M. V. Saveliev TI - Orthogonal decomposition of some affine Lie algebras in terms of their heisenberg subalgebras JO - Teoretičeskaâ i matematičeskaâ fizika PY - 1995 SP - 17 EP - 31 VL - 102 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_1995_102_1_a1/ LA - en ID - TMF_1995_102_1_a1 ER -
%0 Journal Article %A L. A. Ferreira %A D. I. Olive %A M. V. Saveliev %T Orthogonal decomposition of some affine Lie algebras in terms of their heisenberg subalgebras %J Teoretičeskaâ i matematičeskaâ fizika %D 1995 %P 17-31 %V 102 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_1995_102_1_a1/ %G en %F TMF_1995_102_1_a1
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/