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- W2297764547 abstract "Let (V, Q) be a quadratic vector space over a fixed field. Orthogonal group 𝒪(V, Q) is defined as automorphisms on (V, Q). If Q = I, it is 𝒪(V, I) = 𝒪(n). There is a nice result that 𝒪(n) ≅ Aut(𝔬(n)) over ℝ or ℂ, where 𝔬(n) is the Lie algebra of n × n alternating matrices over the field. How about another field The answer is “Yes” if it is GF(2). We show it explicitly with the combinatorial basis ℭ. This is a verification of Steinberg's main result in 1961, that is, Aut(𝔬(n)) is simple over the square field, with a nonsimple exception Aut(𝔬(5)) ≅ 𝒪(5) ≅ 𝔖6." @default.
- W2297764547 created "2016-06-24" @default.
- W2297764547 creator A5030290301 @default.
- W2297764547 date "2014-01-16" @default.
- W2297764547 modified "2023-09-24" @default.
- W2297764547 title "Orthogonal Groups 𝒪(n) overGF(2) as Automorphisms" @default.
- W2297764547 cites W1992437541 @default.
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- W2297764547 doi "https://doi.org/10.1080/00927872.2012.755683" @default.
- W2297764547 hasPublicationYear "2014" @default.
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