  The non-relativistic current algebra approach is analyzed subject to its
application to studying the distribution functions of many-particle systems at
the temperature equilibrium and their stability properties. We show that the
classical Bogolubov generating functional method is a very effective tool for
constructing the irreducible current algebra representations and the
corresponding different generalized measure expansions including collective
variables transform. The effective Hamiltonian operator construction and its
spectrum peculiarities subject to the stability of equilibrium many-particle
systems are discussed.
