Siegel Transformations for even characteristic

Villa, Oliver and Ellers, Erich W. (2005) Siegel Transformations for even characteristic. Linear Algebra and its Applications, 395. pp. 163-174. ISSN 0024-3795

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Let V be a vector space over a field K of even characteristic and ∣K∣ > 3. Suppose K is perfect and π is an element in the special orthogonal group SO(V) with dim B(π)=2d. Then π = ρ1 ⋯ ρd−1κ, where ρj, j = 1 ,…, d − 1, are Siegel transformations and κ ∈ SO(V) with dim B(κ) = 2. The length of π with respect to the Siegel transformations is d if π is unipotent or if dim B (π)/rad B(π) ⩾ 4; otherwise it is d + 1.

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