Observations about the Lie algebra <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e20" altimg="si15.svg"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="fraktur">g</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo linebreak="goodbreak" linebreakstyle="after">⊂</mml:mo><mml:mi mathvariant="fraktur">so</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mn>7</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>, associative 3-planes, and <…
نویسندگان
چکیده
We make several observations relating the Lie algebra g2⊂so(7), associative 3-planes, and so(4) subalgebras. Some are likely well-known but not easy to find in literature, while other results new. show that an element X∈g2 cannot have rank 2, if it has 4 then its kernel is subspace. prove a canonical form theorem for elements of g2. Given 3-plane P R7, we construct subalgebra Θ(P) so(7)=Λ2(R7) isomorphic so(4). This differs from known constructions subalgebras so(7) determined by 3-plane. These NSERC undergraduate research project. The paper written so as be accessible wide audience.
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ژورنال
عنوان ژورنال: Expositiones Mathematicae
سال: 2022
ISSN: ['1878-0792', '0723-0869']
DOI: https://doi.org/10.1016/j.exmath.2022.10.004