The Number of Two-Term Tilting Complexes over Symmetric Algebras with Radical Cube Zero

Adachi, Takahide; Aoki, Toshitaka

doi:10.1007/s00026-022-00587-2

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2022

2024

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Cited by 3 publications

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“…Proof. By [2, Proposition 3.3], it turns out that the Gabriel quiver of is given by adding loops to the double quiver of a quiver ; denote by the quiver of . We also observe that for any arrow of and unless and ; if is an added loop, write .…”

Section: Applications and Examplesmentioning

confidence: 99%

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A symmetry of silting quivers

Aihara

Wang

2023

Glasgow Math. J.

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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).

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Section: Applications and Examplesmentioning

confidence: 99%

“…When is 2-silting finite ( -tilting finite); i.e., , counting the number of elements in is one of the important problems in this area; see [1, 2, 4, 9, 15]. In this context, Theorem 1.4 gives a very useful method to reduce the whole pattern to half of .…”

Section: Introductionmentioning

confidence: 99%