In this paper, we introduce and study a class of algebras which we call ada
algebras. An artin algebra is ada if every indecomposable projective and every
indecomposable injective module lies in the union of the left and the right
parts of the module category. We describe the Auslander-Reiten components of an
ada algebra, showing in particular that its representation theory is entirely
contained in that of its left and right supports, which are both tilted
algebras. Also, we prove that an ada algebra over an algebraically closed field
is simply connected if and only if its first Hochschild cohomology group
vanishes