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anti-automorphism

Glasgow Mathematical Journal (1)

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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).