Algebraic treatment of compactification on noncommutative tori

In this paper we study the compactification conditions of the M theory on D-dimensional noncommutative tori. The main tool used for this analysis is the algebra A(ZD) of the projective representations of the abelian group ZD. We exhibit the explicit solutions in the space of the multiplication algebra of A(ZD), that is the algebra generated by right and left multiplications.