  Based on the work by Smirnov and Zeitlin, we study a simple realization of
the matrix construction of the affine Jacobi varieties. We find that the
realization is given by a classical integrable model, the extended
Lotka-Volterra lattice. We investigate the integrable structure of the
representative for the gauge equivalence class of matrices, which is isomorphic
to the affine Jacobi variety, and make use it to discuss the solvability of the
model.
