Pure semisimple n-cluster tilting subcategories
نویسندگان
چکیده
منابع مشابه
General Heart Construction on a Triangulated Category (I): Unifying t-Structures and Cluster Tilting Subcategories
In the paper of Keller and Reiten, it was shown that the quotient of a triangulated category (with some conditions) by a cluster tilting subcategory becomes an abelian category. After that, Koenig and Zhu showed in detail, how the abelian structure is given on this quotient category, in a more abstract setting. On the other hand, as is well known since 1980s, the heart of any tstructure is abel...
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Tilting theory provides a good method for comparing two categories, such as module categories of finite-dimensional algebras. For an introduction, see e.g. [A]. BGP reflection functors [BGP] give a way of comparing the representation categories of two quivers, where one is obtained from the other by reversing all of the arrows incident with a sink or source. Auslander, Platzeck and Reiten [APR]...
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We study the notion of positive and negative complexity of pairs of objects in cluster categories. The first main result shows that the maximal complexity occurring is either one, two or infinite, depending on the representation type of the underlying hereditary algebra. In the second result, we study the bounded derived category of a cluster tilted algebra, and show that the maximal complexity...
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The purpose of this chapter is to give an introduction to the theory of cluster categories and cluster-tilted algebras, with some background on the theory of cluster algebras, which motivated these topics. We will also discuss some of the interplay between cluster algebras on one side and cluster categories/cluster-tilted algebras on the other, as well as feedback from the latter theory to clus...
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We introduce a new category C, which we call the cluster category, obtained as a quotient of the bounded derived category D of the module category of a finite-dimensional hereditary algebra H over a field. We show that, in the simply-laced Dynkin case, C can be regarded as a natural model for the combinatorics of the corresponding Fomin–Zelevinsky cluster algebra. In this model, the tilting obj...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2020
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2019.11.043