Graded algebras with cyclotomic Hilbert series
Graded algebras with cyclotomic Hilbert series
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DOI：
10.1016/j.jpaa.2021.106764
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发表时间：
2020-05
期刊：
影响因子：
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通讯作者：
A. Borzì;Alessio D'Alì
中科院分区：
文献类型：
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作者：
A. Borzì;Alessio D'Alì
设R是域k上的正分次代数，如果其约化的Hilbert级数的分子的所有根都在单位圆上，我们称R是Hilbert-割圆的。这种环自然地出现在交换代数、数值半群理论和Ehrhart理论中。如果R是标准分次的，我们证明了在附加假设R是Koszul或具有不可约h-多项式的条件下，Hilbert-分圆代数与完全交重合。在Koszul的例子中，这是关于分次代数偏差为零的一些经典结果的结果。
Let R be a positively graded algebra over a field k. We say that R is Hilbert-cyclotomic if the numerator of its reduced Hilbert series has all of its roots on the unit circle. Such rings arise naturally in commutative algebra, numerical semigroup theory and Ehrhart theory. If R is standard graded, we prove that, under the additional hypothesis that R is Koszul or has an irreducible h-polynomial, Hilbert-cyclotomic algebras coincide with complete intersections. In the Koszul case, this is a consequence of some classical results about the vanishing of deviations of a graded algebra.