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Closed ideal structure and cohomological properties of certain radical Banach algebras
Author(s) -
Ghahramani F.,
Read C. J.,
Willis G. A.
Publication year - 2010
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/pdp038
Subject(s) - mathematics , ideal (ethics) , pure mathematics , banach algebra , class (philosophy) , unit interval , jacobson radical , dimension (graph theory) , algebra over a field , discrete mathematics , banach space , ring (chemistry) , law , computer science , chemistry , organic chemistry , artificial intelligence , political science
We further the study of a class of singly generated radical Banach algebras (sometimes called LRRW (Loy, Read, Runde and Willis) algebras after the four authors involved in the original paper) that have compact multiplication and are weakly amenable. First, we characterize the closed ideal structure of these algebras. The closed ideals of an LRRW algebra are identified, and the lattice of closed ideals is shown to be isomorphic to the unit interval. Then we show that LRRW algebras are not approximately amenable and have global homological dimension greater than 1. Furthermore, epimorphisms onto these algebras and derivations from them are continuous.