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arXiv · 1405.4340

Double Lie algebras, semidirect product, and integrable systems

S. Capriotti·H. Montani
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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.

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S. Capriotti, H. Montani. 2014-05-17. Double Lie algebras, semidirect product, and integrable systems. https://arxiv.org/abs/1405.4340

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