ϕ-Biflatness of abstract symmetric Segal algebras

Let A be a Banach algebra and ϕ be a character on A. The notion of ϕ-biflatness for Banach algebras introduced and studied in [6]. In this talk, we characterize the ϕ-biflatness of abstract symmetric Segal algebras. In Particular, we identify ϕ-biflatness of the Lebesgue-Fourier algebra LA(G), where G is a unimodular locally compact group. These results describe a homological property for Segal algebras in the setting of biflatness based on character ϕ.