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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Higher-dimensional virtual diagonals and
ideal cohomology for triangular algebras


Authors: Alan L. T. Paterson and Roger R. Smith
Journal: Trans. Amer. Math. Soc. 349 (1997), 1919-1943
MSC (1991): Primary 47D25, 46H25
MathSciNet review: 1401782
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Abstract: We investigate the cohomology of non-self-adjoint algebras using virtual diagonals and their higher-dimensional generalizations. We show that infinite dimensional nest algebras always have non-zero second cohomology by showing that they cannot possess 2-virtual diagonals. In the case of the upper triangular atomic nest algebra we exhibit concrete modules for non-vanishing cohomology.


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Additional Information

Alan L. T. Paterson
Affiliation: Department of Mathematics, University of Mississippi, University, Mississippi 38677
Email: mmap@sunset.backbone.olemiss.edu

Roger R. Smith
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
Email: rsmith@math.tamu.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-97-01856-4
PII: S 0002-9947(97)01856-4
Keywords: Cohomology, nest algebra, operator algebra, diagonal, virtual diagonal, cocycle
Received by editor(s): July 10, 1995
Received by editor(s) in revised form: November 15, 1995
Additional Notes: Partially supported by grants from the National Science Foundation
Article copyright: © Copyright 1997 American Mathematical Society