Higher-dimensional virtual diagonals and ideal cohomology for triangular algebras

Paterson, Alan; Smith, Roger

doi:10.1090/S0002-9947-97-01856-4

Higher-dimensional virtual diagonals and ideal cohomology for triangular algebras
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by Alan L. T. Paterson and Roger R. Smith PDF

Trans. Amer. Math. Soc. 349 (1997), 1919-1943 Request permission

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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