INTEGRABILITY OF CLASSICAL AFFINE W-ALGEBRAS

INTEGRABILITY OF CLASSICAL AFFINE W-ALGEBRAS

We prove that all classical affine W -algebras W(g; f ), where g is a simple Lie algebra and f is its non-zero nilpotent element, admit an integrable hierarchy of bi-Hamiltonian PDEs, except possibly for one nilpotent conjugacy class in G 2 , one in F 4 , and five in E 8 .

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Veröffentlicht in:Transformation groups 2021-06, Vol.26 (2), p.479-500
Hauptverfasser: SOLE, ALBERTO DE, JIBLADZE, MAMUKA, KAC, VICTOR G., VALERI, DANIELE
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Lie Groups
Mathematics
Mathematics and Statistics
Topological Groups
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Zusammenfassung:We prove that all classical affine W -algebras W(g; f ), where g is a simple Lie algebra and f is its non-zero nilpotent element, admit an integrable hierarchy of bi-Hamiltonian PDEs, except possibly for one nilpotent conjugacy class in G 2 , one in F 4 , and five in E 8 .
ISSN:1083-4362
1531-586X
DOI:10.1007/s00031-021-09645-0