On homological notions of Banach algebras related to a character

A. Sahami

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arXiv · 1401.2558

On homological notions of Banach algebras related to a character

A. Sahami

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Abstract

In this paper, we countinue our work in \cite{11}. We show that $L^{1}(G,w)$ is $\phi_{0}$-biprojective if and only if $G$ is compact, where $\phi_{0}$ is the augmentation character. We introduce the notions of character Johnson amenability and character Johnson contractibility for Banach algebras. We show that $\ell^{1}(S)$ is pseudo-amenable if and only if $\ell^{1}(S)$ is character Johnson-amenable, provided that $S$ is a uniformly locally finite band semigroup. We give some conditions whether $\phi$-biprojectivity ($\phi$-biflatness) of $\ell^{1}(S)$ implies the finiteness (amenability) of $S$, respectively.

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A. Sahami. 2014-01-11. On homological notions of Banach algebras related to a character. https://arxiv.org/abs/1401.2558

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