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- W2799112397 abstract "Let b be a symmetric or alternating bilinear form on a finite-dimensional vector space V. When the characteristic of the underlying field is not 2, we determine the greatest dimension for a linear subspace of nilpotent b-symmetric or b-alternating endomorphisms of V, expressing it as a function of the dimension, the rank, and the Witt index of b. Similar results are obtained for subspaces of nilpotent b-Hermitian endomorphisms when b is a Hermitian form with respect to a non-identity involution. In three situations (b-symmetric endomorphisms when b is symmetric, b-alternating endomorphisms when b is alternating, and b-Hermitian endomorphisms when b is Hermitian and the underlying field has more than 2 elements), we also characterize the linear subspaces with the maximal dimension. Our results are wide generalizations of results of Meshulam and Radwan [7], who tackled the case of a non-degenerate symmetric bilinear form over the field of complex numbers, and recent results of Kokol Bukovšek and Omladič [4], in which the spaces with maximal dimension were determined when the underlying field is the one of complex numbers, the bilinear form b is symmetric and non-degenerate, and one considers b-symmetric endomorphisms." @default.
- W2799112397 created "2018-05-07" @default.
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- W2799112397 date "2019-04-01" @default.
- W2799112397 modified "2023-10-11" @default.
- W2799112397 title "The structured Gerstenhaber problem (I)" @default.
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- W2799112397 doi "https://doi.org/10.1016/j.laa.2018.08.015" @default.
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