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

Algebras Determined by Their Supports