Iacopo Nonis (University of Leeds) – tau-exceptional sequences for representations of quivers over local algebras

Exceptional sequences were first introduced in triangulated categories by the Moscow school of algebraic geometry. Later, Crawley-Boevey and Ringel studied exceptional sequences in the module categories of hereditary finite-dimensional algebras. Motivated by tau-tilting theory introduced by Adachi, Iyama, and Reiten, Jasso’s reduction for tau-tilting modules, and signed exceptional sequences introduced by Igusa and Todorov, Buan and Marsh developed the theory of (signed) tau-exceptional sequences – a natural generalization of (signed) exceptional sequences that behave well over arbitrary finite-dimensional algebras.

In this talk, we will study (signed) tau-exceptional sequences over the algebra 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 (signed) tau-exceptional sequences over Λ can be fully understood in terms of (signed) exceptional sequences over kQ.