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• W2134737960 abstract "The geometrical application of split octonions is considered. The new representation of products of the basis units of split octonionic having David's star shape (instead of the Fano triangle) is presented. It is shown that active and passive transformations of coordinates in octonionic “eight-space” are not equivalent. The group of passive transformations that leave invariant the pseudonorm of split octonions is<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mrow><mml:mi>S</mml:mi><mml:mi>O</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>4</mml:mn><mml:mo>,</mml:mo><mml:mn>4</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>, while active rotations are done by the direct product of<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mrow><mml:mi>O</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>3</mml:mn><mml:mo>,</mml:mo><mml:mn>4</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>-boosts and real noncompact form of the exceptional group<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mrow><mml:msub><mml:mi>G</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math>. In classical limit, these transformations reduce to the standard Lorentz group." @default.
• W2134737960 created "2016-06-24" @default.
• W2134737960 creator A5047937128 @default.
• W2134737960 date "2009-01-01" @default.
• W2134737960 modified "2023-09-25" @default.
• W2134737960 title "Rotations in the Space of Split Octonions" @default.
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• W2134737960 doi "https://doi.org/10.1155/2009/483079" @default.
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