HIGHER-DIMENSIONAL VIRTUAL DIAGONALS AND IDEAL COHOMOLOGY FOR TRIANGULAR ALGEBRAS

Authors
PATERSON ALT SMITH RR
Citation
Alt. Paterson et Rr. Smith, HIGHER-DIMENSIONAL VIRTUAL DIAGONALS AND IDEAL COHOMOLOGY FOR TRIANGULAR ALGEBRAS, Transactions of the American Mathematical Society, 349(5), 1997, pp. 1919-1943
Citations number
18
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Transactions of the American Mathematical Society → ACNP
ISSN journal
00029947
Volume
349
Issue
5
Year of publication
1997
Pages
1919 - 1943
Database
ISI
SICI code
0002-9947(1997)349:5<1919:HVDAIC>2.0.ZU;2-Q
Abstract
We investigate the cohomology of non-self-adjoint algebras using virtu al diagonals and their higher-dimensional generalizations. We show tha t infinite dimensional nest algebras always have non-zero second cohom ology by showing that they cannot possess a-virtual diagonals. In the case of the upper triangular atomic nest algebra we exhibit concrete m odules for non-vanishing cohomology.