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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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##### References:
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