I want to know the origin of the cross product And his relationship with' Groupe compact'
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The cross product makes the vector space $\Bbb{R}^3$ into a $3$-dimensional Lie algebra $\mathfrak{so}_3(\Bbb{R})$. It is the Lie algebra of the compact Lie group $SO_3(\mathbb{R})$. – Dietrich Burde May 03 '18 at 09:38
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@JoséCarlosSantos The linked question doesn't show the relationship with "compact group". – GNUSupporter 8964民主女神 地下教會 May 03 '18 at 09:39
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2The OP should post a new question, only with the second part. The first part really is a duplicate. – Dietrich Burde May 03 '18 at 09:40