http://sites.science.oregonstate.edu/coursewikis/GELG/ 2020-01-26T13:53:42-08:00 http://sites.science.oregonstate.edu/coursewikis/GELG/ http://sites.science.oregonstate.edu/coursewikis/GELG/lib/images/favicon.ico text/html 2016-05-01T19:10:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GELG/book/content/adjointn?rev=1462155000 text/html 2019-05-09T09:51:39-08:00 http://sites.science.oregonstate.edu/coursewikis/GELG/book/content/dynkinn?rev=1557420699 text/html 2016-04-16T14:39:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GELG/book/content/lien?rev=1460842740 text/html 2016-05-07T08:48:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GELG/book/content/rootsn?rev=1462636080 text/html 2016-05-07T11:52:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GELG/book/content/rpropn?rev=1462647120 text/html 2016-03-31T22:41:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GELG/book/content/so2n?rev=1459489260 text/html 2016-04-14T12:05:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GELG/book/content/so31n?rev=1460660700 text/html 2016-04-11T08:41:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GELG/book/content/so3n?rev=1460389260 text/html 2016-04-20T14:38:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GELG/book/content/su2cpn?rev=1461188280 text/html 2016-04-18T15:27:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GELG/book/content/su2n?rev=1461018420 text/html 2016-04-24T20:44:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GELG/book/content/su2repn?rev=1461555840 We have the following basis elements for $\sl(2,\RR)\cong\su(2,\CC')\cong\so(2,1)$, a real form of $\su(2)$: \begin{equation} \sigma_0=\frac12\sigma_z, \quad \sigma_\pm=\frac12(\sigma_x\mp s_y)=\frac12(\sigma_x\pm i\sigma_y), \end{equation} with commutation relations \begin{equation} [\sigma_0,\sigma_\pm]=\pm\sigma_\pm, \quad [\sigma_+,\sigma_-]=2\sigma_0. \label{su2comm} \end{equation} These basis elements also form a basis of the complexified Lie algebra $\su(2)\otimes\CC$. text/html 2016-04-27T11:55:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GELG/book/content/su3n?rev=1461783300 The unitary group $\SU(3)$ consists of all $3\times3$ unitary matrices with determinant $1$, that is \begin{equation} \SU(3) = \{M\in\CC^{3\times3}:M^\dagger M=1, |M|=1\} . \end{equation} The group $\SU(3)$ is the smallest of the unitary groups to be unrelated to the orthogonal groups; it's something new. As is the case for $\su(2)$, the Lie algebra $\su(3)$ consists of all $3\times3$ tracefree, anti-Hermitian matrices, that is \begin{equation} \su(3) = \{A\in\CC^{3\times3}:A^\dagger+A=0, \tr(A…