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... bijection has been extended by Keller and Nicolás in [17] for the bounded derived categories of homologically homologically smooth non-positive differential graded algebras and by Koenig and Yang in =-=[19]-=- for bounded derived categories of finite dimensional algebras over a field. Indeed, they show that in such a category, there is a bijection between silting objects and bounded t-structures whose hear...

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...closed subcategories in modKQ. (l) The set of subclosed subcategories in modKQ. We have given bijections between (a), (b), (c) and (d). Bijections between (g), (h), (i) and (j) are the restriction of =-=[KY]-=- and it is given in [BY, Corollary 4.3] (it is stated for Jacobian algebras, but it holds for any finite dimensional algebra as they point out). Note that compatibilities of mutations and partial orde...

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... subcategory of T containing T is T itself, and HomT (T, T [i]) = 0 for any i > 0 (resp. i 6= 0). We denote the set of silting (resp. tilting) complexes over A as silt(A) (resp. tilt(A)). As noted in =-=[KY]-=-, a silting complex is tilting if and only if it is Nakayama-stable (stable under the Nakayama functor). 2.2 Self-injective Nakayama and Brauer tree algebras Definition 2.4 (see for example [GR, ARS, ...

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... using Lemma 2.1. 2.4. From silting objects to t-structures. Let T be a triangulated category. In this section, we show that under certain conditions silting objects yield t-structures. We refer to =-=[32, 34, 28, 10, 4, 40]-=- for more on this subject. For a silting subcategory P in T , we consider subcategories of T : P[<0]⊥T = {X ∈ T | HomT (P[<0], X) = 0}, P[>0]⊥T = {X ∈ T | HomT (P[>0], X) = 0}. We adopt the notation i...