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Contractible Banach Algebra

A Banach algebra A is called contractible if H^1(A,X)=Z^1(A,X)/B^1(A,X)=0 for all Banach A-bimodules X (Helemskii 1989, 1997).

A C^*-algebra is contractible if and only if it is finite-dimensional (Selivanov 1976).

This entry contributed by Mohammad Sal Moslehian

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References

Helemskii, A. Ya. The Homology of Banach and Topological Algebras. Dordrecht, Netherlands: Kluwer, 1989.Helemskii, A. Ya. "The Homology in Algebra of Analysis." In Handbook of Algebra, Vol. 2. Amsterdam, Netherlands: Elsevier, 1997.Selivanov, Yu. V. "Banach Algebras of Small Global Dimension Zero." Uspekhi Mat. Nauk 31, 227-228, 1976.

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Contractible Banach Algebra

Cite this as:

Weisstein, Eric W., with contributions by Mohammad Sal Moslehian. "Contractible Banach Algebra." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ContractibleBanachAlgebra.html

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