4 papers
Homological dimensions of Schur algebras and an Auslander-type correspondence
Tiago Cruz, Karin Erdmann
We study the homological properties of Schur algebras over a field of positive characteristic , focusing on their interplay with the representation theory of quot…
Ontology Learning and Knowledge Graph Construction: A Comparison of Approaches and Their Impact on RAG Performance
Tiago da Cruz, Bernardo Tavares, Francisco Belo
Retrieval-Augmented Generation (RAG) systems combine Large Language Models (LLMs) with external knowledge, and their performance depends heavily on how that knowledge is represente…
A higher dimensional Auslander-Iyama-Solberg correspondence
Tiago Cruz, Chrysostomos Psaroudakis
In this paper, we prove a higher dimensional version of Auslander-Iyama-Solberg correspondence. Iyama and Solberg have shown a bijection between -minimal Auslander-Gorenstein al…
Relative Auslander--Gorenstein Pairs
Tiago Cruz, Chrysostomos Psaroudakis
In this paper, we introduce and study relative Auslander--Gorenstein pairs. This consists of a finite-dimensional Gorenstein algebra together with a self-orthogonal module that pro…