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Higher-dimensional virtual diagonals and ideal cohomology for triangular algebras |
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| Authors: | Alan L T Paterson Roger R Smith |
| Institution: | Department of Mathematics, University of Mississippi, University, Mississippi 38677 ; Department of Mathematics, Texas A&M University, College Station, Texas 77843 |
| 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. |
| Keywords: | Cohomology nest algebra operator algebra diagonal virtual diagonal cocycle |
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