Notes on the module homological properties of triangular Banach algebras

Document Type : Original Article

Authors

1 Esfarayen University of Technology, Esfarayen, North Khorasan, Iran

2 Department of Mathematics, Faculty of Basic Sciences, Ilam University, Ilam, Iran

3 Department of Mathematics, West Tehran Branch, Islamic Azad University, Tehran, Iran

Abstract

In the current investigation, we find some necessary and sufficient conditions for the triangular Banach algebra $T=

\begin{bmatrix}

A&\mathbb M\\

0&B

\end{bmatrix}$ to be module amenable, module biprojective and module biflat (as $\mathcal U\oplus \mathcal U$-module), where $A$ and $B$ are Banach $\mathcal U$-bimodules and $\mathbb M$ is a Banach $A,B$-module and Banach $\mathcal U$-module with compatible actions. As an application, we show that for an inverse semigroup $S$ with the set of idempotents $E$, under what conditions $\begin{bmatrix}

l^1(S)&\\

& l^1(S)

\end{bmatrix}$ is module amenable, module biprojective and module biflat (as $l^1(E)\oplus l^1(E)$-module).

Keywords

Main Subjects

References

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