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

A. A. Arutyunov ; A. S. Mishchenko

Sbornik. Mathematics, Tome 210 (2019) no. 6, pp. 756-782

Résumé

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.

Détail

Keywords: derivations, Cayley complexes, Hochschild cohomology.
Mots-clés : group algebras, groupoids

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