Title: τ-exceptional sequences for representations of quivers over local algebras. Abstract: In the early 1990s, Crawley-Boevey and Ringel studied exceptional sequences and their mutation in the module categories of hereditary finite-dimensional algebras. More recently, Buan and Marsh introduced τ-exceptional sequences — a natural generalization of exceptional sequences that behaves well over arbitrary finite-dimensional algebras. Together with Hanson, the authors also developed a notion of mutation for τ-exceptional sequences, extending the classical concept of mutation in the hereditary setting. In this talk, we study τ-exceptional sequences and their mutation over algebras of the form Λ = RQ, where R is a finite-dimensional local commutative algebra over an algebraically closed field, and Q is an acyclic quiver. I will explain how τ-exceptional sequences and their mutation over Λ can be fully understood in terms of exceptional sequences and their mutation over kQ.
Given at:
York Algebra Seminar, University of York, UK - June 2025
Algebra and Representation Theory Oberseminar, University of Bonn, Germany - June 2025
Cologne Algebra Seminar, University of Cologne, Germany - June 2025
Maurice Auslander Distinguished Lectures and International Conference, Woods Hole Oceanographic Institution, Quissett Campus Woods Hole, Massachusetts, USA - April 2025
Verona Algebra Seminar, Università degli Studi di Verona , Italy - April 2025
Leeds Algebra Seminar, Univeristy of Leeds, UK - March 2025
Title: τ-exceptional sequences for representations of quivers over local algebras.
Presented at:
IDEAL (Inclusion, Diversity and Equity in Algebra), University of Leeds, UK - October 2025
Advances in Representation Theory of Algebra (ARTA) X - Cologne, Germany - September 2025.