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- W4366328535 abstract "We observe that there exists an associative finite dimensional $mathbb{C}$-algebra $A$ of finite global dimension, such that the bounded derived category $D^b(A)$ of finite dimensional $A$-modules admits an admissible subcategory $mathcal{P}$ with vanishing Grothendieck group $K_0(mathcal{P})$. In other words, $mathcal{P} subseteq D^b(A)$ is a phantom. Using tilting theory, this follows directly from a very recent example of a phantom for a smooth rational surface due to Krah. By work of Aihara & Iyama, this also leads to new examples of presilting objects that cannot be completed to silting objects." @default.
- W4366328535 created "2023-04-20" @default.
- W4366328535 creator A5035832068 @default.
- W4366328535 date "2023-04-17" @default.
- W4366328535 modified "2023-10-17" @default.
- W4366328535 title "A finite dimensional algebra with a phantom (a corollary of an example by J. Krah)" @default.
- W4366328535 doi "https://doi.org/10.48550/arxiv.2304.08417" @default.
- W4366328535 hasPublicationYear "2023" @default.
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