Support varieties for finite tensor categories: Complexity, realization, and connectedness
Support varieties for finite tensor categories: Complexity, realization, and connectedness
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有限张量类别的支持种类：复杂性、实现和连通性
DOI：
10.1016/j.jpaa.2021.106705
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发表时间：
2021
影响因子：
0.8
通讯作者：
Witherspoon, Sarah
中科院分区：
文献类型：
--
作者：
Bergh, Petter Andreas;Plavnik, Julia Yael;Witherspoon, Sarah
提出了有限张量范畴的支持变分理论。首先，我们表明，一个对象的支持变化的尺寸等于一个最小的投影分辨率的增长率，通过测量的Frobenius-Perron维。然后证明了单位物体的支撑分量的每一个圆锥子分量都可以实现为一个物体的支撑分量。最后，我们证明了不可分解对象的支持种类是相互联系的。
We advance support variety theory for finite tensor categories. First we show that the dimension of the support variety of an object equals the rate of growth of a minimal projective resolution as measured by the Frobenius-Perron dimension. Then we show that every conical subvariety of the support variety of the unit object may be realized as the support variety of an object. Finally, we show that the support variety of an indecomposable object is connected.