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2 results

A symmetry of silting quivers
Part of
- Representation theory of rings and algebras
Takuma Aihara, Qi Wang
Journal:

Glasgow Mathematical Journal / Volume 65 / Issue 3 / September 2023

Published online by Cambridge University Press:

26 July 2023, pp. 687-696

Print publication:

September 2023
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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).

Report on the finiteness of silting objects
Part of
- Representation theory of rings and algebras
Takuma Aihara, Takahiro Honma, Kengo Miyamoto, Qi Wang
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 64 / Issue 2 / May 2021

Published online by Cambridge University Press:

07 May 2021, pp. 217-233
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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.