Triangular matrix algebras over affine quasi-hereditary algebras

Abstract

We prove that the triangular matrix algebra Λ=(H0HH) is an affine quasi-hereditary algebra if and only if H is an affine quasi-hereditary algebra. Moreover, the category of Δ-good Λ-modules, the global dimension and the characteristic tilting module of Λ are described by using the corresponding ones of H. In the appendix, we prove that certain centralizer algebra and quotient algebra of an affine quasi-hereditary algebra are affine quasi-hereditary.