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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Nonself-adjoint $2$-graph algebras
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by Adam H. Fuller and Dilian Yang PDF
Trans. Amer. Math. Soc. 367 (2015), 6199-6224 Request permission


We study the structure of weakly-closed nonself-adjoint algebras arising from representations of single vertex $2$-graphs. These are the algebras generated by $2$ isometric tuples which satisfy a certain commutation relation. We show that these algebras have a lower-triangular $3\times 3$ form. The left-hand side of this matrix decomposition is a slice of the enveloping von Neumann algebra generated by the $2$-graph algebra. We further give necessary and sufficient conditions for these algebras themselves to be von Neumann algebras. The paper concludes with further study of atomic representations.
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Additional Information
  • Adam H. Fuller
  • Affiliation: Department of Mathematics, University of Nebraska-Lincoln, Lincoln, Nebraska 68588-0130
  • MR Author ID: 916003
  • ORCID: 0000-0002-9002-0501
  • Email:
  • Dilian Yang
  • Affiliation: Department of Mathematics $\&$ Statistics, University of Windsor, Windsor, Ontario N9B 3P4, Canada
  • MR Author ID: 668010
  • Email:
  • Received by editor(s): June 5, 2013
  • Published electronically: March 26, 2015
  • Additional Notes: The second author was partially supported by an NSERC Discovery grant.
  • © Copyright 2015 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 367 (2015), 6199-6224
  • MSC (2010): Primary 47L55, 47L30, 47L75, 46L05
  • DOI:
  • MathSciNet review: 3356934