拟阵的第一个余切上同调模

IF 0.6 2区 数学 Q3 MATHEMATICS
William Brehm, Alexandru Constantinescu
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引用次数: 1

摘要

给出了拟阵上Stanley-Reisner环的第一个余切上同模的计算公式。对于任意简单复合体,我们给出了$T^1$的多重分量的维数的上界。对于特定的程度,我们证明了当且仅当简单复合体是一个拟阵时,这些界限才成立,从而得到了拟阵的一个新的表征。进一步证明了二阶余切上同调对于非离散矩阵是一个完全不变量。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The first cotangent cohomology module for matroids
We find a combinatorial formula which computes the first cotangent cohomology module of Stanley–Reisner rings associated to matroids. For arbitrary simplicial complexes we provide upper bounds for the dimensions of the multigraded components of $T^1$. For specific degrees we prove that these bounds are reached if and only if the simplicial complex is a matroid, obtaining thus a new characterization for matroids. Furthermore, the graded first cotangent cohomology turns out to be a complete invariant for nondiscrete matroids.
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CiteScore
1.20
自引率
0.00%
发文量
9
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