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fixed latex - it didn't work on my computer
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Peter Shor
Peter Shor
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Regarding Q2: the reduced $C^*$$C^\star$-algebra is functorial wrt homomorphisms with amenable kernels. Indeed, let $N$ be a normal, amenable subgroup of $G$; since the trivial representation of $N$ is weakly contained in the regular representation of $N$ (by amenability), by continuity of induction the regular representation of $G/N$ is weakly contained in the regular representation of $G$, which means that the reduced $C^*$$C^\star$-algebra of $G$ maps onto the one of $G/N$.

Regarding Q2: the reduced $C^*$-algebra is functorial wrt homomorphisms with amenable kernels. Indeed, let $N$ be a normal, amenable subgroup of $G$; since the trivial representation of $N$ is weakly contained in the regular representation of $N$ (by amenability), by continuity of induction the regular representation of $G/N$ is weakly contained in the regular representation of $G$, which means that the reduced $C^*$-algebra of $G$ maps onto the one of $G/N$.

Regarding Q2: the reduced $C^\star$-algebra is functorial wrt homomorphisms with amenable kernels. Indeed, let $N$ be a normal, amenable subgroup of $G$; since the trivial representation of $N$ is weakly contained in the regular representation of $N$ (by amenability), by continuity of induction the regular representation of $G/N$ is weakly contained in the regular representation of $G$, which means that the reduced $C^\star$-algebra of $G$ maps onto the one of $G/N$.

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Alain Valette
Alain Valette
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Regarding Q2: the reduced $C^*$-algebra is functorial wrt homomorphisms with amenable kernels. Indeed, let $N$ be a normal, amenable subgroup of $G$; since the trivial representation of $N$ is weakly contained in the regular representation of $N$ (by amenability), by continuity of induction the regular representation of $G/N$ is weakly contained in the regular representation of $G$, which means that the reduced $C^*$-algebra of $G$ maps onto the one of $G/N$.