APR tilts for path algebra kQ can be realized as the mutation of the quiver Q in \({\mathbb Z}Q\) with respect to the translation. In this paper, we show that we have similar results for the quadratic dual of truncations of n-translation algebras; that is, under certain condition, the n-APR tilts of such algebras are realized as \(\tau \)-mutations. For the dual \(\tau \)-slice algebras with bound quiver \(Q^{\perp }\), we show that their iterated n-APR tilts are realized by the iterated \(\tau \)-mutations in \({\mathbb Z|_{n-1} }Q^{\perp }\).

中文翻译：

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n -APR倾斜和$$ \ tau $$τ-突变

APR对于倾斜路代数千欧可以实现为颤动的突变Q在\（{\ mathbb Z} Q \）相对于所述翻译。在本文中，我们证明对n-平移代数的截断的二次对偶有相似的结果。也就是说，在一定条件下，此类代数的n -APR倾斜被实现为\（\ tau \）-突变。对于具有约束颤动\（Q ^ {\ perp} \）的双\（\ tau \）- slice代数，我们证明了它们的迭代n -APR倾斜是通过\中的迭代\（\ tau \）-突变实现的。 （{\ mathbb Z | _ {n-1}} Q ^ {\ perp} \）。