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On the Liouville-Arnold integrable flows related with quantum algebras and their Poissonian representations

A. M. Samoilenko·Y. A. Prykarpatsky·D. L. Blackmore·A. K. Prykarpatsky
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Abstract

Based on the structure of Casimir elements associated with general Hopf algebras there are constructed Liouville-Arnold integrable flows related with naturally induced Poisson structures on arbitrary co-algebra and their deformations. Some interesting special cases including the oscillatory Heisenberg-Weil algebra related co-algebra structures and adjoint with them integrable Hamiltonian systems are considered.

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A. M. Samoilenko, Y. A. Prykarpatsky, D. L. Blackmore, A. K. Prykarpatsky. 2004-07-01. On the Liouville-Arnold integrable flows related with quantum algebras and their Poissonian representations. https://arxiv.org/abs/nlin/0407003

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