截断路代数同调透明
Truncated path algebras are homologically transparent
摘要：
它示出的路径代数模关系的形式$Λ= KQ/I$，其中$Q$是一个矩阵，$K$的系数字段，和$I \subseteq KQ$的理想所产生的所有路径的一个给定的长度，可以很容易地分析同调，同时显示了丰富的现象。特别是，他们的模块的syzyies，因此他们的有限尺寸，允许光滑的描述方面的$Q$和洛伊长度的$Λ$。对于固定$K$维数模的标准参数化簇的不可约分量上的投射维数分布也是如此。
英文摘要：
It is shown that path algebras modulo relations of the form $Λ= KQ/I$, where $Q$ is a quiver, $K$ a coefficient field, and $I \subseteq KQ$ the ideal generated by all paths of a given length, can be readily analyzed homologically, while displaying a wealth of phenomena. In particular, the syzygies of their modules, and hence their finitistic dimensions, allow for smooth descriptions in terms of $Q$ and the Loewy length of $Λ$. The same is true for the distributions of projective dimensions attained on the irreducible components of the standard parametrizing varieties for the modules of fixed $K$- dimension.
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