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arXiv · 1709.06637

Structure of free semigroupoid algebras

Kenneth R. Davidson·Adam Dor-On·Boyu Li
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Abstract

A free semigroupoid algebra is the closure of the algebra generated by a TCK family of a graph in the weak operator topology. We obtain a structure theory for these algebras analogous to that of free semigroup algebra. We clarify the role of absolute continuity and wandering vectors. These results are applied to obtain a Lebesgue-von Neumann-Wold decomposition of TCK families, along with reflexivity, a Kaplansky density theorem and classification for free semigroupoid algebras. Several classes of examples are discussed and developed, including self-adjoint examples and a classification of atomic free semigroupoid algebras up to unitary equivalence.

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Kenneth R. Davidson, Adam Dor-On, Boyu Li. 2017-09-19. Structure of free semigroupoid algebras. https://arxiv.org/abs/1709.06637

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