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The twisted SU(3) group. Irreducible *-representations of the \(C^*\)-algebra \(C(S_{\mu}U(3))\). (English) Zbl 0706.46054
The author considers unital \(C^*\)-algebras \(C(S_{\mu}U(3))\) generated by nine elements \(u_{ij}\), \(i,j=1,2,3\), satisfying the conditions \[ \sum^{3}_{k=1}u^*_{k\ell}u_{km}=\delta_{\ell m}1,\quad \sum^{3}_{k=1}u_{mk}u^*_{\ell k}=\delta_{m\ell}1,\quad \sum^{3}_{p=1}\sum^{3}_{r=1}\sum^{3}_{s=1}E_{prs}u_{ip}u_{jr} u_{ks}=E_{ijk}1, \] \(i,j,k=1,2,3\), where \(E_{123}=1\), \(E_{132}=E_{213}=-\mu\), \(E_{312}=E_{231}=\mu^ 2\), \(E_{321}=- \mu^ 3\), \(E_{ijk}=0\) otherwise, \(\mu\in (0,1)\). Irreducible *-representations of \(C(S_{\mu}U(3))\) are constructed. It is proved that \(C(S_{\mu}U(3))\) is a type-I \(C^*\)-algebra.
Reviewer: H.Baumgärtel

MSC:
46L60 Applications of selfadjoint operator algebras to physics
22E99 Lie groups
22D99 Locally compact groups and their algebras
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