Ringel duals of affine quasi-hereditary algebras

Abstract

Let H be an affine quasi-hereditary algebra defined in [9] which satisfies the condition given in [6], that is, H is finitely generated over its center. We prove that the Ringel dual R of H is affine quasi-hereditary when H satisfies certain additional condition. Under the same condition, we prove that the double Ringel dual RR of H is graded Morita equivalent to H. In particular, if all the irreducible H-modules have dimension 1, then RR≅H as graded algebras.