"Many-poled" r-matrix Lie algebras, Lax operators, and integrable systems

For each finite-dimensional simple Lie algebra g, starting from a general g⊗g-valued solution r(u, v) of the generalized non-dynamical classical Yang-Baxter equation, we construct "N-poled" infinite-dimensional Lie algebras g~r-,N of g-valued meromorphic functions with the poles in a fixed set of points v1, ..,vN. We apply the constructed algebras to the theory of finite-dimensional integrable systems and theory of soliton equations and obtain with their help the most general form of anisotropic chiral field-type equations as well as the most general form of integrable N-top systems and integrable cases of N interacting Kirchhoff systems.