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
Abstract:
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.References
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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: afuller7@math.unl.edu
- Dilian Yang
- Affiliation: Department of Mathematics $\&$ Statistics, University of Windsor, Windsor, Ontario N9B 3P4, Canada
- MR Author ID: 668010
- Email: dyang@uwindsor.ca
- 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: https://doi.org/10.1090/S0002-9947-2015-06385-5
- MathSciNet review: 3356934