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Journal of Operator Theory

Volume 63, Issue 2, Spring 2010  pp. 389-402.

Certain subalgebras of the tensor product of graph algebras

Authors Amy B. Chambers
Author institution: Department of Mathematics, Tennessee Technological University, Cookeville, TN, 38501, U.S.A.

Summary:  Using an action of the unit circle, we construct a conditional expectation from the tensor product of two graph algebras, C(E1)C(E2), 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 E1 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.


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