Lattices generated by orbits of totally isotropic flats under finite affine-classical groups
type: Item
instance of: scholarly article
title: Lattices generated by orbits of totally isotropic flats under finite affine-classical groups
zbMATH Open document ID: 1158.51003
author: Kaishun Wang
author: Jun Guo
published in: Finite Fields and their Applications
publication date: 2008-08-27T00:00:00Z
review text: The authors construct some families of finite atomic lattices \(\mathcal L\) generated by orbits of totally isotropic flats under finite affine-classical groups in the \(n\)-dimensional spaces \(ACG(n,F_q)\) over the finite field \(F_q\), namely the symplectic group, the unitary group, and the pseudo-symplectic group. \(\mathcal L\) denotes the set of all intersections of the elements of the corresponding orbits. The paper discusses their geometricity, and compute their characteristic polynomials.
reviewed by: Herbert Hotje
Mathematics Subject Classification ID: 51D25
Mathematics Subject Classification ID: 20G40
zbMATH DE Number: 5316914
zbMATH Keywords: affine-classical groups
zbMATH Keywords: totally isotropic flat
zbMATH Keywords: geometric lattice
MaRDI profile type: Publication
full work available at URL: j.ffa.2007.06.004
OpenAlex ID: W2064398535
cites work: Q3050437
cites work: Lattices generated by orbits of subspaces under finite singular unitary group and its characteristic polynomials
cites work: Lattices Generated by Orbits of Subspaces Under Finite Singular Classical Groups and Its Characteristic Polynomials
cites work: Lattices generated by transitive sets of subspaces under finite classical groups I
cites work: Lattices generated by transitive sets of subspaces under finite classical groups II the orthogonal case of odd characteristic
cites work: Lattices generated by transitive sets of subspaces under finite classical groups III the orthogonal case of even characteristic
cites work: Lattices generated by transitive sets of subspaces under finite pseudo-symplectic groups
cites work: On the geometricity of lattices generated by orbits of subspaces under finite classical groups
cites work: Lattices Generated by Orbits of Flats Under Finite Affine Groups
DOI: 10.1016/J.FFA.2007.06.004
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description: scientific article; zbMATH DE number 5316914