Taras Skrypnyk (Bogolyubov Institute for Theoretical Physics, Kyiv, Ukraine)

Dual R-matrix integrability and Thirring-type integrable hierarchies

Abstract:
Using R operator on a Lie algebra g, satisfying modified classical Yang-Baxter equation we define two sets of mutually commuting functions with respect to the initial Lie-Poisson bracket on g^*. We consider in details examples of the Lie algebras g with the "Kostant-Adler-Symmes" and "triangular" decompositions, their R-operators and the corresponding two sets of mutually commuting functions. We discuss application of our construction to the hierarchies of soliton equations and obtain as a partial example integrable generalizations of Thirring model.