Silting mutation in triangulated categories
Silting mutation in triangulated categories
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DOI：
10.1112/jlms/jdr055
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发表时间：
2010-09
期刊：
影响因子：
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通讯作者：
T. Aihara;O. Iyama
中科院分区：
文献类型：
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作者：
T. Aihara;O. Iyama
在代数表示论中，“突变”的概念常常起着重要的作用，有两种情况是众所周知的，即“簇倾斜突变”和“例外突变”。在本文中，我们关注的是倾斜变异，它的一个缺点是它往往是不可能的，即倾斜物体的一些集合不能被替换来获得新的倾斜物体。本文的目的是通过引入淤积物的“淤积突变”作为“倾斜突变”的推广，从而克服这一缺点。我们将发展淤积突变的基本理论。特别地，通过推广Riedtmann-Schofield和Happl-Unger的理论，我们在淤积对象集上引入了一个偏序，并建立了与淤积突变的关系。我们证明了迭代淤积突变对局部代数、遗传代数或正则代数的淤积对象集起传递作用。最后，我们给出了淤积子范畴与某些t-结构之间的一个双射。
In representation theory of algebras the notion of ‘mutation’ often plays important roles, and two cases are well known, that is, ‘cluster tilting mutation’ and ‘exceptional mutation’. In this paper we focus on ‘tilting mutation’, which has a disadvantage that it is often impossible, that is, some of summands of a tilting object cannot be replaced to get a new tilting object. The aim of this paper is to take away this disadvantage by introducing ‘silting mutation’ for silting objects as a generalization of ‘tilting mutation’. We shall develop a basic theory of silting mutation. In particular, we introduce a partial order on the set of silting objects and establish the relationship with ‘silting mutation’ by generalizing the theory of Riedtmann–Schofield and Happel–Unger. We show that iterated silting mutations act transitively on the set of silting objects for local, hereditary or canonical algebras. Finally, we give a bijection between silting subcategories and certain t‐structures.