Some homological results for amalgamated duplication of Banach algebras

Abstract

Let [Formula: see text] and [Formula: see text] be two Banach algebras such that [Formula: see text] is a Banach [Formula: see text]-bimodule with the left and right compatible actions of [Formula: see text] on [Formula: see text]. Let [Formula: see text] be a strongly splitting Banach algebra extension of [Formula: see text] by [Formula: see text]. In this paper, we investigate some homological aspects such as injectivity, projectivity and flatness of [Formula: see text] and give some necessary and sufficient conditions for injectivity, projectivity and flatness of [Formula: see text].