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Dmitrii Korshunov
Dmitrii Korshunov
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Is there a simple characterisation of all rings which appear as $K_0$ of finite groups? By $K_0$ of a finite group $G$ I mean $K_0(\mathbb C[G])$ which in the same as a ring of virtual characters of finite G as far as I understand. So they must be finitely generated free as abelian groups and carry $\lambda$-structure. But what else?

Is there a simple characterisation of all rings which appear as $K_0$ of finite groups? By $K_0$ of a finite group $G$ I mean $K_0(\mathbb C[G])$ which in the same as a ring of virtual characters of finite G as far as I understand. So they must be finitely generated free abelian groups and carry $\lambda$-structure. But what else?

Is there a simple characterisation of all rings which appear as $K_0$ of finite groups? By $K_0$ of a finite group $G$ I mean $K_0(\mathbb C[G])$ which in the same as a ring of virtual characters of finite G. So they must be finitely generated free as abelian groups and carry $\lambda$-structure. But what else?

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Dmitrii Korshunov
Dmitrii Korshunov
  • 2.9k
  • 20
  • 27

Rings that are $K_0$ of finite groups

Is there a simple characterisation of all rings which appear as $K_0$ of finite groups? By $K_0$ of a finite group $G$ I mean $K_0(\mathbb C[G])$ which in the same as a ring of virtual characters of finite G as far as I understand. So they must be finitely generated free abelian groups and carry $\lambda$-structure. But what else?