K-group, zeroth (Ex)
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− | * Show that the group $K_0(R)$ is isomorphic to the group obtain by applying the Grothendieck construction to the abelian monoid of isomorphism classes of finitely generated projective | + | * Show that the group $K_0(R)$ is isomorphic to the group obtain by applying the Grothendieck construction to the abelian monoid of isomorphism classes of finitely generated projective $R$-modules under direct sum. |
− | $R$-modules under direct sum. | + | |
* Compute $K_0(\Cc[S_3])$, where $S_3$ is the [[symmetric group]] on three elements. | * Compute $K_0(\Cc[S_3])$, where $S_3$ is the [[symmetric group]] on three elements. |
Revision as of 14:35, 19 July 2013
- Show that the group is isomorphic to the group obtain by applying the Grothendieck construction to the abelian monoid of isomorphism classes of finitely generated projective -modules under direct sum.
- Compute , where is the symmetric group on three elements.
- Show that the -module of sections of the tangent bundle is finitely generated projective and even stably finitely generated free, but not finitely generated free.