n-representation infinite algebras |
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Authors: | Martin Herschend Osamu Iyama Steffen Oppermann |
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Affiliation: | 1. Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya, 464-8602, Japan;2. Institutt for matematiske fag, NTNU, 7491 Trondheim, Norway |
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Abstract: | From the viewpoint of higher dimensional Auslander–Reiten theory, we introduce a new class of finite dimensional algebras of global dimension n, which we call n-representation infinite. They are a certain analog of representation infinite hereditary algebras, and we study three important classes of modules: n-preprojective, n-preinjective and n -regular modules. We observe that their homological behaviour is quite interesting. For instance they provide first examples of algebras having infinite Ext1-orthogonal families of modules. Moreover we give general constructions of n-representation infinite algebras. |
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Keywords: | 16G20 16G70 18G20 18E30 14F05 |
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