TTF theories induced by two-term tilting complexes and self-injective algebras. (English) Zbl 07787980
Summary: Let \(A\) be an Artin algebra and \(T^\bullet\) a two-term tilting complex of \(A\). We determine when \(T^\bullet\) induces a TTF theory for the module category over \(A\). Next, we assume \(A\) is self-injective. Then we show that \(T^\bullet\) induces a TTF theory for the module category over \(A\) if and only if \(T^\bullet\) is isomorphic to a tilting complex defined by some idempotent in \(A\).
MSC:
| 16G30 | Representations of orders, lattices, algebras over commutative rings |
| 18E30 | Derived categories, triangulated categories (MSC2010) |
| 18E40 | Torsion theories, radicals |
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