On modules of finite complexity over selfinjective artin algebras

Edward L. Green; Dan Zacharia

doi:10.1007/s10468-010-9221-y

On modules of finite complexity over selfinjective artin algebras

Edward L. Green, Dan Zacharia

Department of Mathematics

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

2 Scopus citations

Abstract

In this paper we study Auslander-Reiten sequences of modules with finite complexity over selfinjective artin algebras. In particular, we show that for all eventually Ω-perfect modules of finite complexity, the number of indecomposable non projective summands of the middle term of such sequences is bounded by 4. We also describe situations in which all non projective modules in a connected component of the Auslander-Reiten quiver are eventually Ω-perfect.

Original language	English (US)
Pages (from-to)	857-868
Number of pages	12
Journal	Algebras and Representation Theory
Volume	14
Issue number	5
DOIs	https://doi.org/10.1007/s10468-010-9221-y
State	Published - Oct 2011

Keywords

Auslander-Reiten sequences
Complexity
Selfinjective

ASJC Scopus subject areas

General Mathematics

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10.1007/s10468-010-9221-y

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abstract = "In this paper we study Auslander-Reiten sequences of modules with finite complexity over selfinjective artin algebras. In particular, we show that for all eventually Ω-perfect modules of finite complexity, the number of indecomposable non projective summands of the middle term of such sequences is bounded by 4. We also describe situations in which all non projective modules in a connected component of the Auslander-Reiten quiver are eventually Ω-perfect.",

keywords = "Auslander-Reiten sequences, Complexity, Selfinjective",

author = "Green, {Edward L.} and Dan Zacharia",

note = "Funding Information: Both authors are supported by grants from NSA.",

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N2 - In this paper we study Auslander-Reiten sequences of modules with finite complexity over selfinjective artin algebras. In particular, we show that for all eventually Ω-perfect modules of finite complexity, the number of indecomposable non projective summands of the middle term of such sequences is bounded by 4. We also describe situations in which all non projective modules in a connected component of the Auslander-Reiten quiver are eventually Ω-perfect.

AB - In this paper we study Auslander-Reiten sequences of modules with finite complexity over selfinjective artin algebras. In particular, we show that for all eventually Ω-perfect modules of finite complexity, the number of indecomposable non projective summands of the middle term of such sequences is bounded by 4. We also describe situations in which all non projective modules in a connected component of the Auslander-Reiten quiver are eventually Ω-perfect.

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KW - Complexity

KW - Selfinjective

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ER -

On modules of finite complexity over selfinjective artin algebras

Abstract

Keywords

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