Projectivity of some Banach modules over semiprime Banach algebras

Abstract

Let [Formula: see text] be a semiprime Banach algebra and let [Formula: see text] be a nonzero character on [Formula: see text]. In this paper, we discuss the projectivity of certain left Banach [Formula: see text]-modules in terms of left [Formula: see text]-contractibility of Banach algebras. We also apply our results for the category of quantum group algebras and eventually, we present illustrative examples of the projective left Banach modules over the group algebra [Formula: see text] and the Fourier algebra [Formula: see text] of a locally compact group [Formula: see text].