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Book: LieGroupInverses

See: Math notebook, Define classical Lie groups, Classical Lie groups, Rotations, Exceptional Lie groups

Investigation: Understand Lie groups in terms of the inverses of elements.



The complex special orthogonal group is defined as {$\textrm{SO}(n,\mathbb{C})=\{Q\in \textrm{SL}(n,\mathbb{C})|Q^TQ=QQ^T=I\}$}. The inverse {$Q^{-1}=Q^T$}.

In the case of {$G_2$}, we should be dealing with the octonion transpose, as this is the automorphism group of the octonions.


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Puslapis paskutinį kartą pakeistas 2019 birželio 28 d., 23:46