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In this paper we deduce the existence of analytic structure in a neighbourhood of a maximal ideal M in the spectrum of a commutative Banach algebra, A, from homological assumptions. We assume properties of certain of the cohomology groups Hn(A, A/M), rather than the stronger conditions on the homological dimension of the maximal ideal the first author has considered in previous papers. The conclusion is correspondingly weaker: in the previous work one deduces the existence of a Gel'fand neighbourhood with analytic structure, here we deduce only the existence of a metric neighbourhood with analytic structure. The main method is to consider products of certain co-cycles to deduce facts about the symmetric second cohomology, which is known to be related to the deformation theory of algebras. © Glasgow Mathematical Journal Trust 2000.
Author(s): White MC; Pugach LI
Publication type: Article
Publication status: Published
Journal: Glasgow Mathematical Journal
Year: 2000
Volume: 42
Issue: 1
Pages: 15-24
Print publication date: 01/01/2000
ISSN (print): 0017-0895
ISSN (electronic): 1469-509X
Publisher: Cambridge University Press
URL: http://dx.doi.org/10.1017/S0017089500010028
DOI: 10.1017/S0017089500010028
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