Isomorphisms of algebras associated with directed graphs

By Elias G. Katsoulis, David W. Kribs. 2003

66 citations recorded by the source corpus.

Abstract.Given countable directed graphs G and G′, we show that the associated tensor algebras (G) and (G′) are isomorphic as Banach algebras if and only if the graphs G are G′ are isomorphic. For tensor algebras associated with graphs having no sinks or no sources, the graph forms an invariant for algebraic isomorphisms. We also show that given countable directed graphs G, G′, the free semigroupoid algebras and are isomorphic as dual algebras if and only if the graphs G are G′ are isomorphic. In particular, spatially isomorphic free semigroupoid algebras are unitarily isomorphic. For free semigroupoid algebras associated with locally finite directed graphs with no sinks, the graph forms an invariant for algebraic isomorphisms as well.

Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c83361939d152c3f9fda4d43c3fc20fbeb7f1e2f

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In Algebra and Number Theory

In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Operator Algebras for Multivariable Dynamics (2007, methodology): “A first effort to address the periodic case was the study of isomorphisms between graph algebras [22, 28, 50].”
Schur class operator functions and automorphisms of Hardy algebras (2006, background): “ball of the dual, they need to impose also the assumption that the automorphism is contractive. It then follows from their results that it is, in fact, completely isometric and a w∗-homeomorphism. In [13], Katsoulis and Kribs show that in the setting when Eis determined by a directed graph, Gsay, so”
Free Semigroupoid Algebras (2003, unknown): “O A ] 6 J un 2”