= Cyclic cohomology of a regular lattice
{title2=$\widehat H^0(G,R[G])=\widehat H^{-1}(G,R[G])=0$}
Let $G$ be cyclic and let $R[G]$ carry the regular <permutation action>. Invariants are constant coefficient vectors, which are the images of the norm operator. A vector with coefficient sum zero is the difference of a vector and its cyclic translate, by successively solving the coordinate differences. Thus the norm <group kernel> equals $(\sigma-1)R[G]$. Both cyclic <Tate cohomology> <groups> vanish. This applies to $R=\mathbb Z$ and $R=\mathbb Z_p$, and to finite <direct sums> of regular lattices.
Back to article page
