Integrable triples in semisimple Lie algebras
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...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer Netherlands
2021
|
| Online Access: | https://hdl.handle.net/1721.1/136755 |
| _version_ | 1811083638629990400 |
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| author | De Sole, Alberto Jibladze, Mamuka Kac, Victor G. Valeri, Daniele |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics De Sole, Alberto Jibladze, Mamuka Kac, Victor G. Valeri, Daniele |
| author_sort | De Sole, Alberto |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T12:36:22Z |
| format | Article |
| id | mit-1721.1/136755 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T12:36:22Z |
| publishDate | 2021 |
| publisher | Springer Netherlands |
| record_format | dspace |
| spelling | mit-1721.1/1367552023-12-06T21:54:13Z Integrable triples in semisimple Lie algebras De Sole, Alberto Jibladze, Mamuka Kac, Victor G. Valeri, Daniele Massachusetts Institute of Technology. Department of Mathematics 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. 2021-10-29T18:51:46Z 2021-10-29T18:51:46Z 2021-09-09 2021-09-12T03:08:23Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/136755 Letters in Mathematical Physics. 2021 Sep 09;111(5):117 PUBLISHER_CC en https://doi.org/10.1007/s11005-021-01456-4 Creative Commons Attribution https://creativecommons.org/licenses/by/4.0/ The Author(s) application/pdf Springer Netherlands Springer Netherlands |
| spellingShingle | De Sole, Alberto Jibladze, Mamuka Kac, Victor G. Valeri, Daniele Integrable triples in semisimple Lie algebras |
| title | Integrable triples in semisimple Lie algebras |
| title_full | Integrable triples in semisimple Lie algebras |
| title_fullStr | Integrable triples in semisimple Lie algebras |
| title_full_unstemmed | Integrable triples in semisimple Lie algebras |
| title_short | Integrable triples in semisimple Lie algebras |
| title_sort | integrable triples in semisimple lie algebras |
| url | https://hdl.handle.net/1721.1/136755 |
| work_keys_str_mv | AT desolealberto integrabletriplesinsemisimpleliealgebras AT jibladzemamuka integrabletriplesinsemisimpleliealgebras AT kacvictorg integrabletriplesinsemisimpleliealgebras AT valeridaniele integrabletriplesinsemisimpleliealgebras |