Idempotent subquotients of symmetric quasi-hereditary algebras. (Q610617)

In 1989 \textit{V. Dlab} and \textit{C. M. Ringel} [Proc. Am. Math. Soc. 107, No. 1, 1-5 (1989; Zbl 0681.16015)] showed that over an algebraically closed field every finite-dimensional algebra can be realized as centralizer of some quasi-hereditary algebra. In the present paper this construction is generalized. It is shown that any finite-dimensional algebra can be realized as an idempotent subquotient of a symmetric quasi-hereditary algebra. In particular a rigid symmetric algebra is realized as centralizer subalgebra of a symmetric quasi-hereditary algebra.