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Quasihereditary algebras were introduced by Cline, Parshall and Scott in order to deal with highest weight categories arising from Lie theory. A prototype for quasihereditary algebras are the Schur algebras. Given a finite-dimensional algebra A, we may associate to it a special endomorphism algebra R(A), studied by Auslander and Dlab-Ringel, which we call the ADR algebra of A. The algebra R(A) is a "Schur-like" algebra for A in a naive way. It turns out that the ADR algebra is a strongly quasihereditary algebra in the sense of Ringel. In this talk, we shall describe the neat quasihereditary structure of the ADR algebra. We will also mention other examples of strongly quasihereditary endomorphism algebras arising in representation theory.
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