Limit algebras and integer-valued cocycles, revisited
A triangular limit algebra A is isometrically isomorphic to the tensor algebra of a C*-correspondence if and only if its fundamental relation R(A) is a tree admitting a Z+0-valued continuous and coherent cocycle. For triangular limit algebras which are isomorphic to tensor algebras, we give a very concrete description for their defining C*-correspondence and we show that it forms a complete invariant for isometric isomorphisms between such algebras. A related class of operator algebras is also classified using a variant of the Aho-Hopcroft-Ullman algorithm from computer aided graph theory.
Katsoulis, E. and C. Ramsey. (2016). "Limit algebras and integer-valued cocycles, revisited." Journal of the London Mathematical Society 94, 839-858. https://doi.org/10.1112/jlms/jdw060
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