  Inspired by the group structure on $S^1/ \bbZ$, we introduce a weak hopfish
structure on an irrational rotation algebra $A$ of finite Fourier series. We
consider a class of simple $A$-modules defined by invertible elements, and we
compute the tensor product between these modules defined by the hopfish
structure. This class of simple modules turns out to generate an interesting
commutative unital ring.

Quantum Algebra;High Energy Physics - Theory;Operator Algebras;Representation Theory