Derived equivalences of self-injective 2-Calabi--Yau tilted algebras
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866910364907601920 |
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| author | Kortegaard, Anders S. |
| author_facet | Kortegaard, Anders S. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2205_11309 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Derived equivalences of self-injective 2-Calabi--Yau tilted algebras Kortegaard, Anders S. Representation Theory 16E35, 16G50, 18E10, 18E30 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. |
| title | Derived equivalences of self-injective 2-Calabi--Yau tilted algebras |
| topic | Representation Theory 16E35, 16G50, 18E10, 18E30 |
| url | https://arxiv.org/abs/2205.11309 |