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The global dimension theorem for weighted convolution algebras

Published online by Cambridge University Press:  20 January 2009

F. Ghahramani  and
Yu. V. Selivanov
F. Ghahramani
Affiliation:
University of Manitoba, Winnipeg, Manitoba, Canada, R3T 2N2, Email address: ghahram@cc.umanitoba.ca
Yu. V. Selivanov
Affiliation:
Russian State University of Aviation Technology, Petrovka 27, Moscow 103767, Russia
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Abstract

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We show that the global dimension, dgA, of every commutative Banach algebra A whose radical is a weighted convolution algebra is strictly greater than one. As an application, we see that in this case H2(A, X) ≠ 0 for some Banach A-bimodule X and thus there exists an unsplittable singular extension of the algebra A.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 41 , Issue 2 , June 1998 , pp. 393 - 406
Copyright
Copyright © Edinburgh Mathematical Society 1998

References

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