Functorially finite hearts, simple-minded systems and negative cluster categories
David Pauksztello (Lancaster University, UK)
Abstract: Simple-minded systems (SMSs) were introduced by Koenig-Liu as an abstraction of nonprojective simple modules in stable module categories: the idea was to use SMSs as a way to get around the lack of projective generators to help develop a Morita theory for stable module categories. Recent developments have shown that SMSs in negative Calabi-Yau categories admit mutation theories and combinatorics that are highly suggestive of cluster-tilting theory. In this talk, we explain one such development: that negative Calabi-Yau orbit categories of bounded derived categories of acyclic quivers serve as categorical models of positive Fuss-Catalan combinatorics and one can think of SMSs as negative cluster-tilting objects. Along the way, we will make use of the rather surprising observation that in a triangulated category of finite homological dimension, functorial finiteness of the heart of a t-structure is related to the property of the heart having enough injectives and enough projectives. This is surprising because it says that some feature of how a heart behaves within an ambient triangulated category can be detected intrinsically in the heart. This talk is based on joint work with Raquel Coelho Simoes and David Ploog.
mathematical physicscommutative algebraalgebraic geometryrings and algebrasrepresentation theorysymplectic geometry
Audience: researchers in the topic
Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)
Series comments: Description: Research webinar series
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| Organizers: | Severin Barmeier, Frank Neumann*, Sibylle Schroll* |
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