A Conditional Expectation on the Tensor Product of Exel-Laca algebras


We show that the ultragraph C^*-algebra C^*(\mathcal{G}_1\times\mathcal{G}_2) can be embedded in C^*(\mathcal{G}_1)\otimes C^*(\mathcal{G}_2) as a *-subalgebra. We then use this fact to investigate the existence of a conditional expectation on the tensor product of Exel-Laca algebras onto a certain subalgebra.

DOI Code: 10.1285/i15900932v39n1p25

Keywords: ultragraph $C^*$-algebra; Exel-Laca algebras; conditional expectation

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