On locally compact quantum groups whose algebras are factors

Details On locally compact quantum groups whose algebras are factors On locally compact quantum groups whose algebras are factors

2005-11-03

arxiv.org/abs/math/0511085v1

Mathematics

Operator Algebras

20 pages

Scientific paper

In this paper we are interested in examples of locally compact quantum groups $(M,\Delta)$ such that both von Neumann algebras, $M$ and the dual $\hat{M}$, are factors. There is a lot of known examples such that $(M,\hat{M})$ are respectively of type $(\rm{I}\_{\infty},\rm{I}\_{\infty})$ but there is no examples with factors of other types. We construct new examples of type $(\rm{I}\_{\infty},\rm{II}\_{\infty})$, $(\rm{II}\_{\infty},\rm{II}\_{\infty})$ and $(\rm{III}\_{\lambda},\rm{III}\_{\lambda})$ for each $\lambda\in [0,1]$. Also we show that there is no such example with $M$ or $\hat{M}$ a finite factor.

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