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WHEN IS THE SILTING-DISCRETENESS INHERITED?

Part of: Homological methods Representation theory of rings and algebras General and miscellaneous

Published online by Cambridge University Press:  01 April 2024

TAKUMA AIHARA Open the ORCID record for TAKUMA AIHARA [Opens in a new window]  and
TAKAHIRO HONMA Open the ORCID record for TAKAHIRO HONMA [Opens in a new window]
TAKUMA AIHARA*
Affiliation:
Department of Mathematics Tokyo Gakugei University 4-1-1 Nukuikita-machi, Koganei Tokyo 184-8501 Japan
TAKAHIRO HONMA
Affiliation:
Department of General Education National Institute of Technology (KOSEN), Yuge College Ochi Ehime 794-2593 Japan 99cfqqc9@gmail.com
*
aihara@u-gakugei.ac.jp
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Abstract

We explore when the silting-discreteness is inherited. As a result, one obtains that taking idempotent truncations and homological epimorphisms of algebras transmit the silting-discreteness. We also study classification of silting-discrete simply-connected tensor algebras and silting-indiscrete self-injective Nakayama algebras. This paper contains two appendices; one states that every derived-discrete algebra is silting-discrete, and the other is about triangulated categories whose silting objects are tilting.

Keywords

silting objectsilting-discreteperfect derived categoryrecollementself-injective Nakayama algebra

MSC classification

Primary: 16B50: Category-theoretic methods and results (except as in ) 16G20: Representations of quivers and partially ordered sets 16E45: Differential graded algebras and applications
Type
Article
Information
Nagoya Mathematical Journal , First View , pp. 1 - 23
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Foundation Nagoya Mathematical Journal

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Footnotes

T.A. was partly supported by JSPS Grant-in-Aid for Young Scientists 19K14497.

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