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arXiv · 2001.00193

Perverse Equivalences and Dg-stable Combinatorics

Jeremy Brightbill
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Abstract

Chuang and Rouquier describe an action by perverse equivalences on the set of bases of a triangulated category of Calabi-Yau dimension $-1$. We develop an analogue of their theory for Calabi-Yau categories of dimension $w<0$ and show it is equivalent to the mutation theory of $w$-simple-minded systems. Given a non-positively graded, finite-dimensional symmetric algebra $A$, we show that the differential graded stable category of $A$ has negative Calabi-Yau dimension. When $A$ is a Brauer tree algebra, we construct a combinatorial model of the dg-stable category and show that perverse equivalences act transitively on the set of $|w|$-bases.

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Jeremy Brightbill. 2020-01-01. Perverse Equivalences and Dg-stable Combinatorics. https://arxiv.org/abs/2001.00193

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