Abstract
Let A be an Artin algebra and T∙ a two-term tilting complex of A. We determine when T∙ induces a TTF theory for the module category over A. Next, we assume A is self-injective. Then we show that T∙ induces a TTF theory for the module category over A if and only if T∙ is isomorphic to a tilting complex defined by some idempotent in A.
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Acknowledgements
The author would like to thank the memory of Mitsuo Hoshino for his helpful advise on torsion theories. The author would also like to thank the referee for pointing out the mistake in the previous proof of Theorem 3.5 .
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Presented by: Henning Krause
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Abe, H. TTF Theories Induced by Two-Term Tilting Complexes and Self-Injective Algebras. Algebr Represent Theor 26, 2467–2483 (2023). https://doi.org/10.1007/s10468-022-10191-w
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DOI: https://doi.org/10.1007/s10468-022-10191-w