ИСТИНА

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 alge- bra. 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. The report presents the results obtained jointly with A. Arutyunov, and also with the help of A.I. Shtern