The quasihereditary structure of the Auslander-Dlab-Ringel algebra

TL;DR

This paper explores the quasihereditary structure of the Auslander-Dlab-Ringel algebra, showing how it provides a highest weight theory for any algebra through an axiomatic approach.

Contribution

It introduces an axiomatic framework to analyze the quasihereditary structure of the Auslander-Dlab-Ringel algebra for arbitrary algebras.

Findings

Establishes the quasihereditary nature of $R_A$ using axioms.

Connects the structure of $R_A$ to highest weight theory.

Provides a new perspective on the algebra's properties.

Abstract

Given an arbitrary algebra $A$ we may associate to it a special endomorphism algebra, $R_A$, introduced by Auslander. Dlab and Ringel constructed a heredity chain for $R_A$, proving that every algebra $A$ has an associated highest weight theory. In this paper we investigate the quasihereditary structure of $R_A$ using an axiomatic approach.