Integrable triples in semisimple Lie algebras
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Author(s)
De Sole, Alberto
Jibladze, Mamuka
Kac, Victor G.
Valeri, Daniele
Date Issued
September 9, 2021
Publisher
Springer Netherlands
Citation
Letters in Mathematical Physics. 2021 Sep 09;111(5):117
Version
Final published version
Abstract
Abstract
We classify all integrable triples in simple Lie algebras, up to equivalence. The importance of this problem stems from the fact that for each such equivalence class one can construct the corresponding integrable hierarchy of bi-Hamiltonian PDE. The simplest integrable triple (f, 0, e) in
$${\mathfrak {sl}}_2$$
sl
2
corresponds to the KdV hierarchy, and the triple
$$(f,0,e_\theta )$$
(
f
,
0
,
e
θ
)
, where f is the sum of negative simple root vectors and
$$e_\theta $$
e
θ
is the highest root vector of a simple Lie algebra, corresponds to the Drinfeld–Sokolov hierarchy.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.1007/s11005-021-01456-4
