Elliptic Algebra and Integrable Models for Solitons on Noncommutative Torus {T}

We study the algebra {A}_n, the basis of the Hilbert space {H}_n in terms of θ functions of the positions of n solitons. Then we embed the Heisenberg group as the quantum operator factors in the representation of the transfer matrices of various integrable models. Finally we generalize our result to the generic θ case.