有限偏序集的分步上同调模  

Steply cohomology modules of finite partially ordered sets

作　　者：沃军杰[1] 宋传宁[1] 周才军[1] 

机构地区：[1]上海师范大学数理学院,上海200234

出　　处：《上海师范大学学报（自然科学版）》2009年第2期150-157,共8页Journal of Shanghai Normal University(Natural Sciences)

基　　金：上海师范大学线性代数精品课程

摘　　要：主要研究有限偏序集的二重分步上同调模,讨论该类模的一些性质.举例证明该类模不仅与偏序集的拓扑性质有关,而且与其的组合性质有关.并得到如下两个结果:(i)设P是有限偏序集,x1,x2为P中任意的两个元素,d2为P中所有除x1和x2外的其余元素之和.若x1,x2之间满足x1x2=0,那么P是零调的当且仅当Hx1+x2Hd2(P)=0.(ii)当P是锥型偏序集,设P1,P2为P的两个互不相交的子集,P=P1∪P2,设d1,d2分别等于P1,P2的所有元素之和,那么Hd1Hd2(P)=0.This paper mainly studies the twice - steply cohomology modules of finite partially ordered sets. Some properties of these modules are discussed. Two examples are given which show that the properties of such modules depend not only on the topological properties , but slso on the combinatorial properties of the partially ordered sets. Two results are obtained on follows： （i） Let Pbe a finite partially ordered set, let x1, x2 be any two elements of P, and d2 be the sum of all the elements except x1, x2 in P, if x1 x2 = 0, then P is cyclic ff and only if Hx1 ＋x2 Hd2 （P） = 0; （ii） Let P be a finite cone partially ordered set, P = P1 ∪ P2, P1 ∩ P2 = and d1, d2 be the sum of all the elements in P1, P2 separately. Then Hd1Hd2 （P） =0.

关 键 词：有限偏序集 二重分步上同调模 零调 锥 

分 类 号：O153.3[理学—数学] O154[理学—基础数学]