Higher Auslander algebras admitting trivial maximal orthogonal subcategories

JOURNAL OF ALGEBRA

卷:330

Article

Huang, Zhaoyong¹  Zhang, Xiaojin² 

[1] Nanjing Univ, Dept Math, Nanjing 210093, Jiangsu Prov, Peoples R China

[2] Nanjing Univ Informat Sci & Technol, Coll Math & Phys, Nanjing 210044, Jiangsu Prov, Peoples R China

关键词: Higher Auslander algebras;    Trivial maximal orthogonal subcategories;    Simple modules;    Indecomposable modules;    Homological properties;   

DOI  :  10.1016/j.jalgebra.2010.12.019

来源: Elsevier

【 摘 要 】

In this paper, we prove that A is an (n - 1)-Auslander Artinian algebra with gl.dim Lambda = n (>= 2) admitting a trivial maximal (n - 1)-orthogonal subcategory of mod Lambda if and only if it is Morita equivalent to a finite product of F and [GRAPHICS] where F is a division algebra. In addition, we obtain a necessary condition for an Auslander Artinian algebra admitting a non-trivial maximal 1-orthogonal subcategory. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

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