SO(7) group
= SO(7) group
{c}
{title2=$SO(7)$}
= SO(7)
{c}
{synonym}
The compact <group> of real seven-by-seven <orthogonal matrices> with <determinant> one. Its <Lie algebra> has <B3 root system>. Its simply connected double cover is the <Spin group> $\operatorname{Spin}(7)$; the eight-dimensional <spin representation> belongs to that cover and does not descend to <SO(7)>.