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arXiv · 2205.11309

Derived equivalences of self-injective 2-Calabi--Yau tilted algebras

Anders S. Kortegaard
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Abstract

Consider a $k$-linear Frobenius category $\mathscr{E}$ with a projective generator such that the corresponding stable category $\mathscr{C}$ is 2-Calabi--Yau, Hom-finite with split idempotents. Let $l,m\in\mathscr{C}$ be maximal rigid objects with self-injective endomorphism algebras. We will show that their endomorphism algebras $\mathscr{C}(l,l)$ and $\mathscr{C}(m,m)$ are derived equivalent. Furthermore we will give a description of the two-sided tilting complex which induces this derived equivalence.

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BibTeXRIS

Anders S. Kortegaard. 2022-05-23. Derived equivalences of self-injective 2-Calabi--Yau tilted algebras. https://doi.org/10.1112/blms.12982

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