On the ideal structure of the Fourier-Stieltjes algebra of certain groups

Timo Siebenand

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arXiv · 2005.01772

On the ideal structure of the Fourier-Stieltjes algebra of certain groups

Timo Siebenand

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Abstract

We determine the structure of the weak*-closed $G$-invariant ideals in the Fourier-Stieltjes algebra $B(G)$ of certain groups $G$ by means of a $K$-theoretical obstruction. The groups to which this applies are groups whose only irreducible unitary representations that are not weakly contained in the left regular representation are class-one representations. In particular, this is the case for the groups $\mathrm{SL}(2,\mathbb{R})$ and $\mathrm{SL}(2,\mathbb{C})$, which we consider as explicit examples.

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Timo Siebenand. 2020-05-04. On the ideal structure of the Fourier-Stieltjes algebra of certain groups. https://arxiv.org/abs/2005.01772

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