Quivers with relations for symmetrizable Cartan matrices I: Foundations

• 成果类型: Article
• 署名作者: Geiss, Christof; Leclerc, Bernard; Schroeer, Jan
• 署名单位: Universidad Nacional Autonoma de Mexico; Universite de Caen Normandie; Centre National de la Recherche Scientifique (CNRS); Institut Universitaire de France; University of Bonn
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-016-0705-1
• 发表日期: 2017
• 页码: 61-158
• 关键词: maximal rigid objects; preprojective algebras; REPRESENTATIONS; convolution; Operators; functors; rings

摘要

We introduce and study a class of Iwanaga-Gorenstein algebras defined via quivers with relations associated with symmetrizable Cartan matrices. These algebras generalize the path algebras of quivers associated with symmetric Cartan matrices. We also define a corresponding class of generalized preprojective algebras. For these two classes of algebras we obtain generalizations of classical results of Gabriel, Dlab-Ringel, and Gelfand-Ponomarev. In particular, we obtain new representation theoretic realizations of all finite root systems without any assumption on the ground field.