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Ali Taghavi
Ali Taghavi
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Let $G$ be a locally compact group. Put $I(G)=\ker: C^{*}(G) \to C_{r}^{*} (G)$, the kernel of the canonical morphism.

What type of $C^{*}$ algebras can not be in the formisomorphic to $I(G)$, for some locally compact group $G$?In particular finit dimensional, unital, abelian,. etc? Is there any reference for characterization of such algebras?

Let $G$ be a locally compact group. Put $I(G)=\ker: C^{*}(G) \to C_{r}^{*} (G)$, the kernel of the canonical morphism.

What type of $C^{*}$ algebras can not be in the form $I(G)$ for some locally compact group $G$?In particular finit dimensional, unital, abelian,. etc? Is there any reference for characterization of such algebras?

Let $G$ be a locally compact group. Put $I(G)=\ker: C^{*}(G) \to C_{r}^{*} (G)$, the kernel of the canonical morphism.

What type of $C^{*}$ algebras can not be isomorphic to $I(G)$, for some locally compact group $G$?In particular finit dimensional, unital, abelian,. etc? Is there any reference for characterization of such algebras?

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Ali Taghavi
Ali Taghavi
  • 356
  • 8
  • 31
  • 123

The kernel of $C^{*}(G)\to C_{r}^{*}(G)$

Let $G$ be a locally compact group. Put $I(G)=\ker: C^{*}(G) \to C_{r}^{*} (G)$, the kernel of the canonical morphism.

What type of $C^{*}$ algebras can not be in the form $I(G)$ for some locally compact group $G$?In particular finit dimensional, unital, abelian,. etc? Is there any reference for characterization of such algebras?