A smooth version of Johnson's problem on derivations of group algebras

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Abstract

We give a description of the algebra of outer derivations of the group algebra of a finitely presented discrete group in terms of the Cayley complex of the groupoid of the adjoint action of the group. This problem is a smooth version of Johnson's problem on derivations of a group algebra. We show that the algebra of outer derivations is isomorphic to the one-dimensional compactly supported cohomology group of the Cayley complex over the field of complex numbers. Bibliography: 34 titles.

About the authors

Andronick Aramovich Arutyunov

Moscow Institute of Physics and Technology (State University)

Email: andronick.arutyunov@gmail.com
Candidate of physico-mathematical sciences, no status

Alexandr Sergeevich Mishchenko

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Email: asmish@mech.math.msu.su
Doctor of physico-mathematical sciences, Professor

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