## Tannaka-Krein duality for compact matrix pseudogroups. Twisted SU(N) groups.(English)Zbl 0664.58044

The notion of concrete monoidal $$W^*$$-category is introduced and investigated. A generalization of the Tannaka-Krein duality theorem is proved. It leads to new examples of compact matrix pseudogroups. Among them we have twisted SU(N) groups denoted by $$S_{\mu}U(N)$$. It is shown that the representation theory for $$S_{\mu}U(N)$$ is similar to that of SU(N): irreducible representations are labeled by Young diagrams and formulae for dimensions and multiplicity are the same as in the classical case.

### MSC:

 58H05 Pseudogroups and differentiable groupoids
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### References:

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