“School of Mathematics”
Back to Papers HomeBack to Papers of School of Mathematics
Paper IPM / M / 18027 | ||||||||||||
|
||||||||||||
Abstract: | ||||||||||||
Let Λ be an artin algebra and M be an n-cluster tilting subcategory of Λ-mod with n≥2. From the viewpoint of higher homological algebra, a question that naturally arose in [17] is when M induces an n-cluster tilting subcategory of Λ-Mod. In this paper, we answer this question and explore its connection to Iyamaâ??s question on the finiteness of n-cluster tilting subcategories of Λ-mod. In fact, our theorem reformulates Iyamaâ??s question in terms of the vanishing of Ext; and highlights its relation with the rigidity of filtered colimits of M. Also, we show that Add(M) is an n-cluster tilting subcategory of Λ-Mod if and only if Add(M) is a maximal n-rigid subcategory of Λ-Mod if and only if M is of finite type if and only if Ext1Λ(lim. Moreover, we present several equivalent conditions for Iyamaâ??s question which shows the relation of Iyama's question with different subjects in representation theory such as purity and covering theory.
Download TeX format |
||||||||||||
back to top |