On the Geometricity of Lattices Generated by Orbits of Subspaces Under Finite Classical Groups
On the Geometricity of Lattices Generated by Orbits of Subspaces Under Finite Classical Groups
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DOI：
10.1006/jabr.2001.8819
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发表时间：
2001-09
影响因子：
0.9
通讯作者：
Y. Huo;Z. Wan
中科院分区：
文献类型：
--
作者：
Y. Huo;Z. Wan
设Fnq是有限域Fq上的n维向量空间，Gn是Fq上的n次经典群之一。设M是Gn下的子空间的任意轨道。用L表示M中子空间的交的子空间集合，并假设F nq的子空间空集的交是F nq本身。通过对L进行普通包含或逆包含排序，得到两个格。本文讨论了它们何时形成几何格。
Abstract Let F nq be the n-dimensional vector space over the finite field F q and let Gn be one of the classical groups of degree n over F q. Let M be any orbit of subspaces under Gn. Denote by L the set of subspaces which are intersections of subspaces in M and assume the intersection of the empty set of subspaces of F nq is F nq itself. By ordering L by ordinary or reverse inclusion, two lattices are obtained. This paper discusses when they form geometric lattices.