Structure of free semigroupoid algebras
Operator Algebras
2019-06-14 v2 Functional Analysis
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.
Keywords
Cite
@article{arxiv.1709.06637,
title = {Structure of free semigroupoid algebras},
author = {Kenneth R. Davidson and Adam Dor-On and Boyu Li},
journal= {arXiv preprint arXiv:1709.06637},
year = {2019}
}
Comments
65 pages, 1 figure. Accepted to JFA