Mutation in triangulated categories and rigid Cohen-Macaulay modules

Osamu Iyama; Yuji Yoshino

Mutation in triangulated categories and rigid Cohen-Macaulay modules

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arxiv math/0607736 v3 pith:WWTLXUDI submitted 2006-07-28 math.RT math.AC

Osamu Iyama , Yuji Yoshino This is my paper · ORCID

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keywords cohen-macaulaymodulesmutationrigidtriangulatedableauslander-reiten-serrecategories

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abstract

We introduce the notion of mutation of $n$-cluster tilting subcategories in a triangulated category with Auslander-Reiten-Serre duality. Using this idea, we are able to obtain the complete classifications of rigid Cohen-Macaulay modules over certain Veronese subrings.

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From green mutation to $\mathrm{X}$-evolution: flows and foliations on cluster complexes
math.RT 2025-01 conditional novelty 7.0 of 10

Introduces a piecewise-linear flow on cluster complexes whose leaves generalize green mutation, proving these complexes are spheres for Dynkin quivers and contractible for Euclidean quivers.

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