  A completely integrable dynamical system in discrete time is studied by means
of algebraic geometry. The system is associated with factorization of a linear
operator acting in a direct sum of three linear spaces into a product of three
operators, each acting nontrivially only in a direct sum of two spaces, and the
following reversing of the order of factors. There exists a reduction of the
system interpreted as a classical field theory in 2+1-dimensional space-time,
the integrals of motion coinciding, in essence, with the statistical sum of an
inhomogeneous 6-vertex free-fermion model on the 2-dimensional kagome lattice
(here the statistical sum is a function of two parameters). Thus, a connection
with the ``local'', or ``generalized'', quantum Yang--Baxter equation is
revealed.
