  The theory of cluster algebras of S. Fomin and A. Zelevinsky has assigned a
fan to each Dynkin diagram. Then A. Buan, R. Marsh, M. Reineke, I. Reiten and
G. Todorov have generalized this construction using arbitrary quivers on Dynkin
diagrams. In the special case of the unioriented quiver of type A, we describe
the cohomology ring of the toric variety associated to this fan. A natural base
is obtained and an explicit rule is given for the product of any two
generators.
