# Relative dominant dimension and quasi-hereditary covers

Every finite-dimensional algebra can be written as the endomorphism algebra of a projective module over a quasi-hereditary algebra. Moreover, every finite-dimensional algebra over an algebraically closed field admits a (split) quasi-hereditary cover in the sense of Rouquier. So we may wonder how closely connected the module category of a finite-dimensional algebra is to the module category of one of its quasi-hereditary covers.

In this talk, we discuss how a generalisation of dominant dimension can be used as a tool to measure the quality of (split) quasi-hereditary covers of Noetherian algebras and how it can be used to construct new quasi-hereditary covers.