Katsoulis, Elias G.Ramsey, Christopher2020-12-152022-05-312022-05-312016Katsoulis, 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/jdw060https://hdl.handle.net/20.500.14078/2097A 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.393.58KBPDFenAll Rights Reservedoperator algebrasArticle Post-Printhttps://doi.org/10.1112/jlms/jdw060