Аннотация:A description of the algebra of outer derivations of a group algebra of a finitely presented discrete group is
given in terms of the Cayley complex of the groupoid of the adjoint action of the group. This task is a smooth
version of Johnson’s problem concerning the derivations of a group algebra. It is shown that the algebra of
outer derivations is isomorphic to the group of the one-dimensional cohomology with compact supports of the
Cayley complex over the field of complex numbers.
On the other hand the group of outer derivation is isomorphic to the one dimensional Hochschild cohomology
of the group algebra. Thus the whole Hochschild cohomology group can be described in terms of the cohomology
of the classifying space of the groupoid of the adjoint action of the group under the suitable assumption of the
finiteness of the supports of cohomology groups.
