论文标题
棱镜和类型$ a $的前置代数的三角剖分
Triangulations of prisms and preprojective algebras of type $A$
论文作者
论文摘要
我们表明，在$π_{n} $上不可分解的两项预选复合物，$ a_ {n} $的预定代数为$ a_ {n} $，与内部$ n $ -simplices一起进行培养，prism $δ__{n} \ timesΔ_{1} $Δ_{1} $，$ n $ n $ n $ n $ -n $ -n $ simplex的产物。我们进一步表明，这引起了$δ_{n} \ timesδ_{1} $的三角剖分与$π_{n} $上的两项淤积络合物之间的两次射击，使得三角形的三角形的bistellar翻转对应于两项淤积络合物的突变。这些射击显示与涉及对称群的已知射击兼容。
We show that indecomposable two-term presilting complexes over $Π_{n}$, the preprojective algebra of $A_{n}$, are in bijection with internal $n$-simplices in the prism $Δ_{n} \times Δ_{1}$, the product of an $n$-simplex with a 1-simplex. We show further that this induces a bijection between triangulations of $Δ_{n} \times Δ_{1}$ and two-term silting complexes over $Π_{n}$ such that bistellar flips of triangulations correspond to mutations of two-term silting complexes. These bijections are shown to compatible with the known bijections involving the symmetric group.
