On certain strongly quasihereditary algebras - Gomes Cipriano Nabais Conde, T (2016)
Given a finite-dimensional algebra A we may associate to it a special endomorphism algebra, RA, introduced by Auslander. The algebra RA is a "Schur-like" algebra for A: it contains A as an idempotent subalgebra (up to Morita equivalence) and it is quasihereditary with respect to a particular heredity chain. The main purpose of this thesis is to describe the quasihereditary structure of RA which arises from such heredity chain, and to investigate the corresponding Ringel dual of RA. It turns out that RA belongs to a certain class of strongly quasihereditary algebras defined axiomatically, which we call ultra strongly quasihereditary algebras. We derive the key properties of ultra strongly quasihereditary algebras, and give examples of other algebras which fit into this setting.