CERTAIN SUBALGEBRAS OF THE TENSOR PRODUCT OF GRAPH ALGEBRAS

Using an action of the unit circle, we construct a conditional expectation from the tensor product of two graph algebras, C* (E(1)) circle times C* (E(2)), onto a defined subalgebra B. In addition, we make precise the required hypotheses for this subalgebra B to be isomorphic to the graph algebra C* (E) for the graph E defined using the Cartesian products of the vertex and edge sets of the graphs El and E2. We study two concrete examples of the conditional expectation constructed for the general case, and we discuss the ideas of index and Paschke crossed product by an endomorphism.