Two-term silting and $\tau$-cluster morphism categories

Erlend D. B{\o}rve

Two-term silting and $\tau$-cluster morphism categories

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arxiv 2110.03472 v5 pith:EXZV4N7E submitted 2021-10-07 math.RT math.CT

Erlend D. B{o}rve This is my paper · ORCID

classification math.RTmath.CT

keywords categoriesclustermorphismreductionsiltingalgebrasbuan--hansonbuan--marsh

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abstract

We generalise $\tau$-cluster morphism categories to the setting of non-positive dg algebras with finite dimensional cohomology in all degrees. The compatibility of silting reduction with support $\tau$-tilting reduction will be an essential ingredient when linking our definition to those of Buan--Marsh and Buan--Hanson.

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Mutation of $\tau$-exceptional sequences for acyclic quivers over local algebras
math.RT 2025-05 conditional novelty 6.0 of 10

For algebras R⊗kQ with R local and Q acyclic, BHM mutation of complete τ-exceptional sequences coincides with classical mutation, and the braid group acts transitively.

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