A geometric model of tube categories
A geometric model of tube categories
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DOI：
10.1016/j.jalgebra.2012.04.009
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发表时间：
2010-11
影响因子：
0.9
通讯作者：
K. Baur;Robert J. Marsh
中科院分区：
文献类型：
--
作者：
K. Baur;Robert J. Marsh
我们根据边界上有标记点的环带中定向弧的同伦类给出了管类别的几何模型。特别地，我们根据相应弧之间的负几何交集数来解释不可分解对象之间的1度可拓群的维数，从而将管的簇类别中的可拓群的描述给出几何解释为管中可拓群的对称版本。我们表明，类似的结果适用于 A∞∞ 类型的线性定向箭袋的有限维表示。
We give a geometric model for a tube category in terms of homotopy classes of oriented arcs in an annulus with marked points on its boundary. In particular, we interpret the dimensions of extension groups of degree 1 between indecomposable objects in terms of negative geometric intersection numbers between corresponding arcs, giving a geometric interpretation of the description of an extension group in the cluster category of a tube as a symmetrized version of the extension group in the tube. We show that a similar result holds for finite dimensional representations of the linearly oriented quiver of type A∞∞.