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ISSN : 1226-0657

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Vol.30 No.1

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(Co)homology of a Generalized Matrix Banach Algebra

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2023, v.30 no.1, pp.15-24
https://doi.org/https://doi.org/10.7468/jksmeb.2023.30.1.15
M. Akbari
F. Habibian
M., A. , & F., H. (2023). (Co)homology of a Generalized Matrix Banach Algebra. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 30(1), 15-24, https://doi.org/https://doi.org/10.7468/jksmeb.2023.30.1.15

Abstract

In this paper, we show that bounded Hochschild homology and cohomology of associated matrix Banach algebra 𝔊(𝔄, R, S, 𝔅) to a Morita context 𝔐(𝔄, R, S, 𝔅, { }, [ ]) are isomorphic to those of the Banach algebra 𝔄. Consequently, we indicate that the n-amenability and simplicial triviality of 𝔊(𝔄, R, S, 𝔅) are equivalent to the n-amenability and simplicial triviality of 𝔄.

keywords
Banach algebra, cohomology, homology, Morita equivalence

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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