Partly Free Algebras from Directed Graphs

Details Partly Free Algebras from Directed Graphs Partly Free Algebras from Directed Graphs

2003-09-24

arxiv.org/abs/math/0309393v1

Operator Theory: Advances and Applications, Birkhauser-Verlag Basel/Switzerland, 149 (2004), 381-393.

Mathematics

Operator Algebras

12 pages, Proc. Intl. Workshop on Operator Theory and its Applications 2002, to appear

Scientific paper

We say that a nonselfadjoint operator algebra is partly free if it contains a free semigroup algebra. Motivation for such algebras occurs in the setting of what we call free semigroupoid algebras. These are the weak operator topology closed algebras generated by the left regular representations of semigroupoids associated with finite or countable directed graphs. We expand our analysis of partly free algebras from previous work and obtain a graph-theoretic characterization of when a free semigroupoid algebra with countable graph is partly free. This analysis carries over to norm closed quiver algebras. We also discuss new examples for the countable graph case.

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