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A symmetry of silting quivers

Part of: Representation theory of rings and algebras

Published online by Cambridge University Press:  26 July 2023

Takuma Aihara Open the ORCID record for Takuma Aihara [Opens in a new window]  and
Qi Wang
Takuma Aihara
Affiliation:
Department of Mathematics, Tokyo Gakugei University, Koganei, Tokyo 184-8501, Japan
Qi Wang*
Affiliation:
Yau Mathematical Sciences Center, Tsinghua University, Hai Dian District, Beijing 100084, China
*
Corresponding author: Qi Wang; Email: infinite-wang@outlook.com
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Abstract

We investigate symmetry of the silting quiver of a given algebra which is induced by an anti-automorphism of the algebra. In particular, one shows that if there is a primitive idempotent fixed by the anti-automorphism, then the 2-silting quiver ($=$ the support $\tau$-tilting quiver) has a bisection. Consequently, in that case, we obtain that the cardinality of the 2-silting quiver is an even number (if it is finite).

Keywords

silting objectsilting mutationsilting quiversupport τ-tilting modulesupport τ-tilting quiveranti-automorphism

MSC classification

Primary: 16G20: Representations of quivers and partially ordered sets
Secondary: 16G60: Representation type (finite, tame, wild, etc.)
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 65 , Issue 3 , September 2023 , pp. 687 - 696
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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Footnotes

TA was partly supported by JSPS Grant-in-Aid for Young Scientists 19K14497. QW was partly supported by JSPS Grant-in-Aid for Young Scientists 20J10492.

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