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Symmetry

dr. undefined
in Linear Algebra and Group Theory

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Are special unitary groups as SU(5) symmetrical? Orthogonal groups are symmetrical but are unitary groups too?

Are special unitary groups as SU(5) symmetrical? Orthogonal groups are symmetrical but are unitary groups too?

Symmetrical how? Do you mean that transposing takes the group to itself?

=Uncool-

Do you mean, are the generators of the group represented by symmetric matrices? If so, then no. The generators obey [math]T_a^\dagger=T_a[/math] so you need to transpose and take the complex conjugate. Orthogonal group generators are symmetric because the relation is [math]T_a^T=T_a[/math].

Do you mean, are the generators of the group represented by symmetric matrices? If so, then no. The generators obey [math]T_a^\dagger=T_a[/math] so you need to transpose and take the complex conjugate. Orthogonal group generators are symmetric because the relation is [math]T_a^T=T_a[/math].

Uh. Orthogonal group generators are antisymmetric.

=Uncool-

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