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STRONGLY QUASI-HEREDITARY ALGEBRAS AND REJECTIVE SUBCATEGORIES

Part of: Representation theory of rings and algebras General theory of categories and functors

Published online by Cambridge University Press:  27 February 2018

MAYU TSUKAMOTO
MAYU TSUKAMOTO*
Affiliation:
Department of Mathematics, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan email m13sa30m19@st.osaka-cu.ac.jp
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Abstract

Ringel’s right-strongly quasi-hereditary algebras are a distinguished class of quasi-hereditary algebras of Cline–Parshall–Scott. We give characterizations of these algebras in terms of heredity chains and right rejective subcategories. We prove that any artin algebra of global dimension at most two is right-strongly quasi-hereditary. Moreover we show that the Auslander algebra of a representation-finite algebra $A$ is strongly quasi-hereditary if and only if $A$ is a Nakayama algebra.

MSC classification

Primary: 16G10: Representations of Artinian rings 18A40: Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)
Type
Article
Information
Nagoya Mathematical Journal , Volume 237 , March 2020 , pp. 10 - 38
Copyright
© 2018 Foundation Nagoya Mathematical Journal  

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Footnotes

This work is supported by Grant-in-Aid for JSPS Fellowships No. H15J09492.

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