*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.