dr. undefined Posted July 24, 2012 Share Posted July 24, 2012 Are special unitary groups as SU(5) symmetrical? Orthogonal groups are symmetrical but are unitary groups too? Link to comment Share on other sites More sharing options...

uncool Posted July 24, 2012 Share Posted July 24, 2012 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- Link to comment Share on other sites More sharing options...

Severian Posted July 24, 2012 Share Posted July 24, 2012 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]. Link to comment Share on other sites More sharing options...

uncool Posted July 24, 2012 Share Posted July 24, 2012 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- Link to comment Share on other sites More sharing options...

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