11 citations · 29 across the 8 of their papers we have counts for
8 papers · 1 filter
Comparing self-dual corings, Frobenius corings and Ringel self-duality
Tomasz Brzeziński, Teresa Conde, Steffen Koenig +1
Self-dual corings and self-dual algebra extensions are classified and these (self-)dualities are compared with Ringel (self-)duality, revealing fundamental differences. To each cor…
Exact Borel subalgebras, idempotent quotients and idempotent subalgebras
Teresa Conde, Julian Külshammer
This article studies the compatibility of Koenig's notion of an exact Borel subalgebra of a quasi-hereditary or, more generally, standardly stratified algebra with taking idempoten…
Triangular decompositions: Reedy algebras and quasi-hereditary algebras
Teresa Conde, Georgios Dalezios, Steffen Koenig
Finite-dimensional Reedy algebras form a ring-theoretic analogue of Reedy categories and were recently proved to be quasi-hereditary. We identify Reedy algebras with quasi-heredita…
A functorial approach to rank functions on triangulated categories
Teresa Conde, Mikhail Gorsky, Frederik Marks +1
We study rank functions on a triangulated category via its abelianisation . We prove that every rank function on can be i…
All quasihereditary algebras with a regular exact Borel subalgebra
Teresa Conde
Not every quasihereditary algebra has an exact Borel subalgebra. A theorem by Koenig, Külshammer and Ovsienko asserts that there always exists a quasihereditary alge…
Gabriel-Roiter measure, representation dimension and rejective chains
Teresa Conde
The Gabriel-Roiter measure is used to give an alternative proof of the finiteness of the representation dimension for Artin algebras, a result established by Iyama in 2002. The con…
The Ringel dual of the Auslander-Dlab-Ringel algebra
Teresa Conde, Karin Erdmann
The ADR algebra of a finite-dimensional algebra is a quasihereditary algebra. In this paper we study the Ringel dual of . We prove that $\mathcal{…
The quasihereditary structure of the Auslander-Dlab-Ringel algebra
Teresa Conde
Given an arbitrary algebra we may associate to it a special endomorphism algebra, , introduced by Auslander. Dlab and Ringel constructed a heredity chain for , provin…