Double Lie algebras, semidirect product, and integrable systems

2014/05/17 by Santiago Capriotti, Capriotti, S., H. Montani +1
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1405.4340

openalex publication_date 2014/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study integrable systems on double Lie algebras in absence of Ad-invariant bilinear form by passing to the semidirect product with the τ-representation. We show that in this stage a natural Ad-invariant bilinear form does exist, allowing for a straightforward application of the AKS theory, and giving rise to Manin triple structure, thus bringing the problem to the realm of Lie bialgebras and Poisson-Lie groups.

Citations

• Curvatures of left invariant metrics on lie groups

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