Abstract
Let \(\Lambda \) be an Artin algebra and \(M\in \) mod\(\Lambda \). It is well-known that the Bongartz’s Theorem plays an important role in the representation theory of Artin algebras. In this paper, we investigate the relative version of the Bongartz’s Theorem in the bounded homotopy category \(K^{b}(\text {add}M)\) and construct a Bongartz’s completion for an \(\text {add}M\)-relative presilting complex in \(K^{b}(\text {add}M)\) such that it becomes an \(\text {add}M\)-relative silting complex. Finally, we give some applications.
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Communicated by Bernhard Keller.
This work was supported by National Natural Science Foundation of China (11671126).
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Hu, Y., Yao, H. The Bongartz’s Theorem on the Homotopy Category. Bull. Iran. Math. Soc. 45, 667–681 (2019). https://doi.org/10.1007/s41980-018-0158-y
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DOI: https://doi.org/10.1007/s41980-018-0158-y