The structured Gerstenhaber problem (III)

2019/08/11 by Clément de Seguins Pazzis, Pazzis, Clément de Seguins
Engineering · Mathematics · #Material Science and Thermodynamics #Differential Equations and Boundary Problems

paper · pdf · doi:10.48550/arxiv.1908.03934

Abstract

Let b be a symmetric bilinear form on a finite-dimensional vector space over a field with characteristic 2. Here, we determine the greatest possible dimension of a linear subspace of nilpotent b-symmetric or b-alternating endomorphisms of V, expressing it as a function of the dimension, the rank, the Witt index of b, and an additional invariant in a very special case.

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• The structured Gerstenhaber problem (I)
• The structured Gerstenhaber problem (II)
• A dimension bound for subspaces of symmetric bilinear forms in terms of the number of different ranks
• Dimension bounds for constant rank subspaces of symmetric bilinear forms\n over a finite field
• Rank-related dimension bounds for subspaces of bilinear forms over finite fields