# Symmetry

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

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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?

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

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

Uh. Orthogonal group generators are antisymmetric.

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