  The work of A.V. Borisov, A.E. Pavlov, Dynamics and Statics of Vortices on a
Plane and a Sphere - I (Reg. & Ch. Dynamics, 1998, Vol. 3, No 1, p.28-39)
introduces a naive description of dynamics of point vortices on a plane in
terms of variables of distances and areas which generate Lie-Poisson structure.
Using this approach a qualitative description of dynamics of point vortices on
a plane and a sphere is obtained in the works Dynamics of Three Vortices on a
Plane and a Sphere - II. General compact case by A.V. Borisov, V.G. Lebedev
(Reg. & Ch. Dynamics, 1998, Vol. 3, No 2, p.99-114), Dynamics of three vortices
on a plane and a sphere - III. Noncompact case. Problem of collaps and
scattering by A.V. Borisov, V.G. Lebedev (Reg. & Ch. Dynamics, 1998, Vol. 3, No
4, p.76-90). In this paper we consider more formal constructions of the general
problem of n vortices on a plane and a sphere. The developed methods of
algebraization are also applied to the classical problem of the reduction in
the three-body problem.
