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JOURNALS // Contemporary Mathematics. Fundamental Directions // Archive

CMFD, 2024 Volume 70, Issue 3, Pages 356–374 (Mi cmfd545)

Triviality of outer derivations in $\ell_p(G)$ for one class of groups

A. A. Arutyunova, A. V. Naianzinb

a V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow, Russia
b Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Russia

Abstract: In this paper, we study derivations in group rings completed by various types of norms. The main attention is paid to the class of groups in which conjugations act in a controlled manner in some sense. Using the method of identifying derivations and characters on some category, we obtain an alternative way of proving that for this class of groups all derivations are inner.

Keywords: derivation on algebras, outer derivation, inner derivation, character.

UDC: 517.28+512.552

DOI: 10.22363/2413-3639-2024-70-3-356-374



© Steklov Math. Inst. of RAS, 2024