Hereditary noetherian categories of positive Euler characteristic
Hereditary noetherian categories of positive Euler characteristic
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DOI：
10.1007/s00209-006-0938-6
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发表时间：
2006-03
影响因子：
0.8
通讯作者：
H. Lenzing;I. Reiten
中科院分区：
文献类型：
--
作者：
H. Lenzing;I. Reiten
我们开发了任意域 k 上具有塞尔对偶性的遗传诺特范畴的基础，其中平滑射影曲线 overk 上的相干滑轮范畴作为主要例子，其他例子来自有限维代数的表示理论。查看此类类别的正确方法是考虑可能非交换的平滑射影曲线上的相干滑轮。我们为每个这样的类别概念定义函数场和欧拉特征，确定其 Auslander-Reiten 分量并研究稳定和半稳定丛以获得适当的度概念。我们通过将这些与（局部有界）遗传代数的有限维表示相关联，为正欧拉特征的情况提供了遗传诺特范畴的完整分类，该代数的基础值颤动承认正加性函数。
We develop the fundamentals of hereditary noetherian categories with Serre duality over an arbitrary fieldk, where the category of coherent sheaves over a smooth projective curve overkserves as the prime example and others are coming from the representation theory of finite dimensional algebras. The proper way to view such a category is to think of coherent sheaves on a possibly non-commutative smooth projective curve. We define for each such category notions like function field and Euler characteristic, determine its Auslander-Reiten components and study stable and semistable bundles for an appropriate notion of degree. We provide a complete classification of hereditary noetherian categories for the case of positive Euler characteristic by relating these to finite dimensional representations of (locally bounded) hereditaryk-algebras whose underlying valued quiver admits a positive additive function.