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).

中文翻译：

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淤泥颤动的对称性

我们研究给定代数的淤颤的对称性，这是由代数的反自同构引起的。特别是，如果存在由反自同构固定的本原幂等，则 2-淤泥箭袋（$=$支持$\tau$ -倾斜箭袋）具有二等分。因此，在这种情况下，我们得到 2 淤泥颤抖的基数是偶数（如果它是有限的）。