| 仿射酉群作用下的面轨道生成的格 |
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| 引用本文： | 王兆飞,张贺,梅瑞.仿射酉群作用下的面轨道生成的格[J].数学的实践与认识,2009,39(5). |
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| 作者姓名： | 王兆飞 张贺 梅瑞 |
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| 作者单位： | 河北北方学院纬一中路理学院数学系,河北张家口,075000 |
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| 摘 要： | 设AUG(n,Fq2)是Fq2上的n维仿射酉空间,AUn(Fq2)是Fq2上的n次仿射酉群,设M(m,r)是AUn(Fq2)作用下的(m,r)面的轨道.用L(m,r)表示M(m,r)中面的交生成的集合.讨论了各轨道生成的集合之间的包含关系,一个面属于M(m,r)生成的集合的条件,以及L(m,r)是几何格的充要条件.
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| 关 键 词： | 仿射酉群 仿射酉空间 轨道 几何格 |
Lattices Generated by Orbits of Flats Under Finite Affine Unitary |
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| WANG Zhao-fei,ZHANG He,MEI Rui.Lattices Generated by Orbits of Flats Under Finite Affine Unitary[J].Mathematics in Practice and Theory,2009,39(5). |
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| Authors: | WANG Zhao-fei ZHANG He MEI Rui |
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| Abstract: | Let AUG(n,Fq2) be the n-dimensional affine unitary space over the finite field Fq2,let AUn(Fq2) be the affine unitary group of degree n over Fq2.M(m,r) any orbit of(m,r) flats in under AUG(n,Fq2).Denote by L(m,r) the sets of flats which are intersections of flats in M(m,r).this paper discusses the relations of inclusion among sets generated by different orbits,a condition for which a flat is an element of set generated by the given orbit,and how the sets generated by orbits form the geometric lattices. |
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| Keywords: | affine unitary group affine unitary space orbit geometric lattices |
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