Auslander-Reiten theory for modules of finite complexity over self-injective algebras

Otto Kerner; Dan Zacharia

doi:10.1112/blms/bdq082

Auslander-Reiten theory for modules of finite complexity over self-injective algebras

Otto Kerner, Dan Zacharia

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

In this paper, we describe the shapes of the stable components containing modules with finite complexity over a self-injective finite-dimensional algebra over an algebraically closed field. We prove that the associated orbit graph of each such component is either a Dynkin diagram (finite or infinite), or an extended Dynkin diagram.

Original language	English (US)
Pages (from-to)	44-56
Number of pages	13
Journal	Bulletin of the London Mathematical Society
Volume	43
Issue number	1
DOIs	https://doi.org/10.1112/blms/bdq082
State	Published - Feb 2011

ASJC Scopus subject areas

Mathematics(all)

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10.1112/blms/bdq082

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abstract = "In this paper, we describe the shapes of the stable components containing modules with finite complexity over a self-injective finite-dimensional algebra over an algebraically closed field. We prove that the associated orbit graph of each such component is either a Dynkin diagram (finite or infinite), or an extended Dynkin diagram.",

author = "Otto Kerner and Dan Zacharia",

note = "Funding Information: Received 11 September 2009; revised 10 May 2010; published online October 26, 2010. 2000 Mathematics Subject Classification 16G70 (primary), 16D50, 16E05 (secondary). The second author is supported by a grant from NSA.",

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Auslander-Reiten theory for modules of finite complexity over self-injective algebras

Abstract

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