Iacopo Nonis, University of Leeds
tau-exceptional sequences for representations of quivers
over local algebras
Abstract: 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.