Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

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

Request Permissions   Purchase Content 
 

 

Nonself-adjoint $ 2$-graph algebras


Authors: Adam H. Fuller and Dilian Yang
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
Published electronically: March 26, 2015
MathSciNet review: 3356934
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 47L55, 47L30, 47L75, 46L05

Retrieve articles in all journals with MSC (2010): 47L55, 47L30, 47L75, 46L05


Additional Information

Adam H. Fuller
Affiliation: Department of Mathematics, University of Nebraska-Lincoln, Lincoln, Nebraska 68588-0130
Email: afuller7@math.unl.edu

Dilian Yang
Affiliation: Department of Mathematics $&$ Statistics, University of Windsor, Windsor, Ontario N9B 3P4, Canada
Email: dyang@uwindsor.ca

DOI: https://doi.org/10.1090/S0002-9947-2015-06385-5
Keywords: Nonself-adjoint 2-graph algebra, free semigroup algebra, structure projection, $3\times 3$ matrix form, analytic.
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.
Article copyright: © Copyright 2015 American Mathematical Society