Isomorphisms of algebras associated with directed graphs

Details Isomorphisms of algebras associated with directed graphs Isomorphisms of algebras associated with directed graphs

2003-09-22

arxiv.org/abs/math/0309363v4

Math. Ann. 330, (2004), 709-728

Mathematics

Operator Algebras

22 pages. Accepted for publication in the Mathematische Annalen. New introduction. (Old) Section 4 has been omitted

Scientific paper

In this paper we verify that the graph forms a complete invariant for Banach algebra isomorphisms of tensor algebras of graphs. For tensor algebras associated with countable directed graphs having no sinks the graph forms an invariant for algebraic isomorphisms as well. The graph also forms a complete invariant for w*-bicontinuous isomorphisms of free semigroupoid algebras. For free semigroupoid algebras associated with countable directed locally finite graphs with no sinks, the graph also forms an invariant for algebraic isomorphisms.

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