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arXiv · 1601.03423

Limit algebras and integer-valued cocycles, revisited

Elias Katsoulis·Chris Ramsey
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Abstract

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.

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Elias Katsoulis, Chris Ramsey. 2016-01-13. Limit algebras and integer-valued cocycles, revisited. https://doi.org/10.1112/jlms%2Fjdw060

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