Author:
De Sole Alberto,Jibladze Mamuka,Kac Victor G.,Valeri Daniele
Abstract
AbstractWe 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.
Funder
PRIN 2017
Sapienza Università di Roma
Shota Rustaveli National Science Foundation
Bert and Ann Kostant fund
Simons collaboration grant
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Statistical and Nonlinear Physics
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