Tuesday, October 25, 15:00, 7.527
The ADR algebra and other strongly quasihereditary algebras
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 struture of
the ADR algebra. We will also mention other examples of strongly
quasihereditary endomorphism algebras arising in representation theory.