left φ-biprojectivity of some classes of abstract segal algebras

In this paper, we investigate left φ-biprojectivity of segal algebras and abstract segal algebras. we show that for some abstract segal algebras with some mild conditions left φ-biprojectivity is equivalent with left φ-contractibility. also we characterize left φ- biprojectivity of a segal algebra s(g) in the terms of compactness of g, where g is a locally compact group. we introduce a class of abstract segal algebras among triangular banach algebras. we show that some abstract segal algebras related to triangular banach algebras are not biprojective.