Structure of free semigroupoid algebras

Kenneth R. Davidson, Adam Dor-On, Boyu Li

Research output: Contribution to journalArticlepeer-review

Abstract

A free semigroupoid algebra is the WOT-closure of the algebra generated by a TCK family of a graph. 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.

Original languageEnglish
Pages (from-to)3283-3350
Number of pages68
JournalJournal of Functional Analysis
Volume277
Issue number9
DOIs
StatePublished - 1 Nov 2019
Externally publishedYes

Bibliographical note

Funding Information:
The first author was partially supported by a grant 2018-03973 from NSERC.The second author was partially supported by an Ontario Trillium Scholarship.

Publisher Copyright:
© 2019 Elsevier Inc.

Keywords

  • Free semigroupoid algebras
  • Graph algebras
  • Road colouring
  • Wandering vectors and absolute continuity

ASJC Scopus subject areas

  • Analysis

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