Auslander–Reiten sequences, locally free sheaves and Chebysheff polynomials
Auslander–Reiten sequences, locally free sheaves and Chebysheff polynomials
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Auslander–Reiten 序列、局部自由滑轮和切比雪夫多项式
作者：
R. Martínez;D. Zacharia
设R是域K上的n + 1元外代数.本文研究了Pn上线性R-模范畴和凝聚层范畴的某些子范畴的Auslander-Reiten代数。当n > 1时，我们证明了直到shift，这些Auslander-Reiten箭图的所有连通分量除了一个之外都是${f Z} A_{infty}$-型线我们还研究了射影n-空间Pn（n > 1）上的局部自由层，证明了每个连通分支至多包含一个秩小于n的不可分解的局部自由层。最后，利用有限维代数理论的结果，我们构造了一族不可分解的任意大秩的局部自由层，其中秩可以使用第二类Chebysheff多项式来计算。
Let R be the exterior algebra in n + 1 variables over a field K. We study the Auslander–Reiten quiver of the category of linear R-modules, and of certain subcategories of the category of coherent sheaves over Pn. If n > 1, we prove that up to shift, all but one of the connected components of these Auslander–Reiten quivers are translation subquivers of a ${f Z} A_{infty}$-type quiver. We also study locally free sheaves over the projective n-space Pn for n > 1 and we show that each connected component contains at most one indecomposable locally free sheaf of rank less than n. Finally, using results from the theory of finite-dimensional algebras, we construct a family of indecomposable locally free sheaves of arbitrary large ranks, where the ranks can be computed using the Chebysheff polynomials of the second kind.