# Free Semigroupoid Algebras

@article{Kribs2003FreeSA, title={Free Semigroupoid Algebras}, author={D. Kribs and S. Power}, journal={arXiv: Operator Algebras}, year={2003} }

Every countable directed graph generates a Fock space Hilbert space and a family of partial isometries. These operators also arise from the left regular representations of free semigroupoids derived from directed graphs. We develop a structure theory for the weak operator topology closed algebras generated by these representations, which we call free semigroupoid algebras. We characterize semisimplicity in terms of the graph and show explicitly in the case of finite graphs how the Jacobsonâ€¦Â Expand

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