Canad. Math. Bull. 51(2008), 81-85
Printed: Mar 2008
The positive cohomology groups of a finite group acting on a ring
vanish when the ring has a norm one element. In this note we give
explicit homotopies on the level of cochains when the group is cyclic,
which allows us to express any cocycle of a cyclic group
as the coboundary of an explicit cochain.
The formulas in this note are closely related to the effective problems considered in previous joint work
with Eli Aljadeff.
group cohomology, norm map, cyclic group, homotopy
20J06 - Cohomology of groups
20K01 - Finite abelian groups [For sumsets, see 11B13 and 11P70]
16W22 - Actions of groups and semigroups; invariant theory
18G35 - Chain complexes [See also 18E30, 55U15]