CERTAIN SUBALGEBRAS OF THE TENSOR PRODUCT OFGRAPH ALGEBRAS

摘要

Using an action of the unit circle, we construct a conditional ex-pectation from the tensor product of two graph algebras, C~*(E_1 ) 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~* (ε) for the graph ε defined using the Cartesian products of the vertex and edge sets of the graphs E_1 and E_2. 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.