dr. undefined 0 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 post Share on other sites

uncool 231 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 post Share on other sites

Severian 410 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 post Share on other sites

uncool 231 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 post Share on other sites

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