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Special Quasigraded Lie Algebras and Integrable Hamiltonian Systems

Authors:	T Skrypnyk

Institution:	(1) Bogoliubov Institute for Theoretical Physics, Institute of Mathematics of NASU, Metrologichna st. 14-b, Kiev, 03143, Ukraine

Abstract:	We construct a family of special quasigraded Lie algebras $\widetilde{\mathsf{g}}_{F}$ of functions of one complex variables with values in finite-dimensional Lie algebra $\mathfrak{g}$ , labeled by the special 2-cocycles F on $\mathsf{g}$ . The main property of the constructed Lie algebras $\widetilde{\mathsf{g}}_{F}$ is that they admit Kostant-Adler-Symes scheme. Using them we obtain new integrable finite-dimensional Hamiltonian systems and new hierarchies of soliton equations.

Keywords:	Quasigraded Lie algebras Integrable Hamiltonian systems
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