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Homology and cohomology groups of commutative Banach algebras and analytic polydiscs

Lookup NU author(s): Dr Michael White

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Abstract

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.


Publication metadata

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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