Geometry of Semilinear Embeddings

DOI10.1142/9465zbMath1332.51004OpenAlexW4231080074MaRDI QIDQ5256626

M. A. Pankov

Publication date: 19 June 2015

Full work available at URL: https://doi.org/10.1142/9465

zbMATH Keywords

Johnson graphGrassmann graphsemilinear isomorphismsemicollineation\(m\)-independent subsetopposite division ringPGL-subsetsemilinear \(m\)-embeddingstrong semilinear embedding

Mathematics Subject Classification ID

Linear codes (general theory) (94B05) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Linear transformations, semilinear transformations (15A04) Research exposition (monographs, survey articles) pertaining to linear algebra (15-02) Synthetic treatment of fundamental manifolds in projective geometries (Grassmannians, Veronesians and their generalizations) (51M35) Research exposition (monographs, survey articles) pertaining to geometry (51-02)

Related Items (15)

On the distance between linear codes ⋮ Top-heavy phenomena for transformations ⋮ Chow's theorem for linear codes ⋮ Wigner's type theorem in terms of linear operators which send projections of a fixed rank to projections of other fixed rank ⋮ Isometric embeddings of polar Grassmannians and metric characterizations of their apartments ⋮ Geometric version of Wigner's theorem for Hilbert Grassmannians ⋮ The graphs of non-degenerate linear codes ⋮ On embeddings of Grassmann graphs in polar Grassmann graphs ⋮ Adjacency preserving maps between exterior powers of vector spaces ⋮ Cores and independence numbers of Grassmann graphs ⋮ The graph of 4-ary simplex codes of dimension 2 ⋮ The graphs of projective codes ⋮ Orthogonal apartments in Hilbert Grassmannians ⋮ Automorphisms of Grassmann graphs over a residue class ring ⋮ On the \(P_3\)-hull numbers of \(q\)-Kneser graphs and Grassmann graphs

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