Higher simple-minded systems in negative Calabi-Yau categories.

Jeremy Brightbill (UC Santa Barbara, USA)

09-Dec-2021, 16:00-17:00 (2 years ago)

Abstract: Higher simple-minded systems are collections of objects in a negative Calabi-Yau category whose behavior mimics that of simple modules. Under certain hypotheses the collection of all simple-minded systems admits a theory of mutations. In this talk, we shall discuss how to construct many examples of negative Calabi-Yau categories using the so-called "dg-stable category". For a concrete example, we consider the dg-stable category of a negatively-graded Brauer tree algebra. Using a combinatorial model, we classify the simple-minded systems of this category and describe its mutation theory.

mathematical physicscommutative algebraalgebraic geometryrings and algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

( slides )


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