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Report on the finiteness of silting objects

Part of: Representation theory of rings and algebras

Published online by Cambridge University Press:  07 May 2021

Takuma Aihara ,
Takahiro Honma ,
Kengo Miyamoto  and
Qi Wang
Takuma Aihara
Affiliation:
Department of Mathematics, Tokyo Gakugei University, 4-1-1 Nukuikita-machi, Koganei, Tokyo184-8501, Japan ([email protected])
Takahiro Honma
Affiliation:
Graduate School of Mathematics, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku, Tokyo162-8601, Japan ([email protected])
Kengo Miyamoto
Affiliation:
Department of Computer and Information Science, Ibaraki University, 4-12-1, Nakanarusawa-cho, Hitachi, Ibaraki 316-8511, Japan ([email protected])
Qi Wang
Affiliation:
Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Suita, Osaka565-0871, Japan ([email protected])
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Abstract

We discuss the finiteness of (two-term) silting objects. First, we investigate new triangulated categories without silting object. Second, we study two classes of $\tau$-tilting-finite algebras and give the numbers of their two-term silting objects. Finally, we explore when $\tau$-tilting-finiteness implies representation-finiteness and obtain several classes of algebras in which a $\tau$-tilting-finite algebra is representation-finite.

Keywords

silting objectsupport τ-tilting moduleτ-tilting-finite

MSC classification

Primary: 16G20: Representations of quivers and partially ordered sets
Secondary: 16G60: Representation type (finite, tame, wild, etc.)
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 64 , Issue 2 , May 2021 , pp. 217 - 233
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Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society

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