Additivity of homological dimensions for a class of Banach algebras

Author: Tabaldyev, S.

Source: Functional Analysis and Its Applications, Volume 40, Number 3, July 2006 , pp. 244-246(3)

Publisher: Springer

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Abstract:

Let Ω be a metrizable compact space. Suppose that its derived set of some finite order is empty. Let B be a unital Banach algebra, and let <EquationSource Format="TEX"><![CDATA[ $$widehat otimes $$ ]]></EquationSource> stand for the projective tensor product. We prove the additivity formulas dg C(Ω)B <EquationSource Format="TEX"><![CDATA[ $$widehat otimes $$ ]]></EquationSource> =dgB and db C(Ω) <EquationSource Format="TEX"><![CDATA[ $$widehat otimes $$ ]]></EquationSource> B=dbC(Ω)+dbB for the global homological dimension and the homological bidimension. Thus these formulas are true for a new class of commutative Banach algebras in addition to those considered earlier by Selivanov.

Keywords: global homological dimension; homological bidimension; projective Banach module; metrizable compact space; derived set

Document Type: Research article

DOI: http://dx.doi.org/10.1007/s10688-006-0040-1

Affiliations: 1: Email: seytek@newmail.ru

Publication date: 2006-07-01