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首页> 外文期刊>Journal of combinatorial algebra >Stanley–Reisner rings for symmetric simplicial complexes, $G$-semimatroids and Abelian arrangements
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Stanley–Reisner rings for symmetric simplicial complexes, $G$-semimatroids and Abelian arrangements

机译：Stanley-Reisner环对称的单纯复合物,G -semimatroids美元和阿贝耳安排

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We extend the notion of face rings of simplicial complexes and simplicial posets to the case of finite-length (possibly infinite) simplicial posets with a group action. The action on the complex induces an action on the face ring, and we prove that the ring of invariants is isomorphic to the face ring of the quotient simplicial poset under a mild condition on the group action.We also identify a class of actions on simplicial complexes that preserve the homotopical Cohen–Macaulay property under quotients. When the acted-upon poset is the independence complex of a semimatroid, the h-polynomial of the ring of invariants can be read off the Tutte polynomial of the associated group action. Moreover, in this case an additional condition on the action ensures that the quotient poset is Cohen–Macaulay in characteristic 0 and every characteristic that does not divide an explicitly computable number. This implies the same property for the associated Stanley–Reisner rings. In particular, this holds for independence posets and rings associated to toric, elliptic and, more generally, $(p,q)$-arrangements. As a byproduct, we prove that posets of connected components (also known as posets of layers) of such arrangements are Cohen–Macaulay with the same condition on the characteristic.
机译：我们扩展的概念面临单形的戒指配合物和单体的偏序集的情况下有限长(可能是无限的)单纯偏序集和一群行动。复杂的诱发动作表面上环,我们证明不变量的戒指同构的脸环商温和条件下单纯的偏序集上组织行动。保留的单纯的复合物homotopical Cohen-Macaulay财产商。独立semimatroid复杂,h-polynomial环的不变量阅读了相关的多项式组织行动。附加条件的行动确保商中Cohen-Macaulay偏序集0和每个特征特征没有划分一个明确的可计算的数字。这意味着相同的属性相关联Stanley-Reisner戒指。为独立相关的偏序集和戒指环面的,椭圆,更普遍的是,(p, q)安排美元。偏序集的连接组件(也称偏序集的层)这样的安排Cohen-Macaulay相同的条件的特点。

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