n-平移代数、平凡扩张与预投射代数

n-Translation algebras, trivial extensions and preprojective algebras

Koszul稳定n-平移代数的对偶τ-切片代数是一类拟(n-1)-Fano代数.本文给出一个分次代数成为稳定n-平移代数的对偶τ-切片代数的判别法,并证明Koszul稳定n-平移代数的齐次对偶τ-切片代数的预投射代数等于其二次对偶的扭平凡扩张的二次对偶,作为其推论,本文得到对偶切片代数的导出范畴与其预投射代数的非交换射影概型的导出范畴等价.

Dual τ-slice algebra of a stable n-translation algebra is a class of quasi（n-1）-Fano algebras. In this paper, we give a criteria of when a graded algebra becomes a dual τ-slice algebra of a stable n-translation algebra, using Loewy matrices. We prove that the preprojective algebra of homogeneous dual τ-slice algebra is the quadratic dual of a twisted trivial extension of its quadratic dual, we also obtain the equivalences between the derived category of the module category of the dual τ-slice algebra and the derived category of the category of the noncommutative projective schemes of the preprojective algebra as a consequence.