Projectivity of some Banach modules over semiprime Banach algebras.

Let 풜 be a semiprime Banach algebra and let φ be a nonzero character on 풜. In this paper, we discuss the projectivity of certain left Banach 풜-modules in terms of left φ-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 L1(G) and the Fourier algebra A(G) of a locally compact group G. [ABSTRACT FROM AUTHOR]