On certain strongly quasihereditary algebras

Thesis

Given a finite-dimensional algebra A we may associate to it a special endomorphism algebra, R_A, introduced by Auslander. The algebra R_A 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 R_A which arises from such heredity chain, and to investigate the corresponding Ringel dual of R_A. It turns out that R_A 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.

Authors: Gomes Cipriano Nabais Conde, T

• DOI: 10.5287/ora-qxgmokq2b
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford