Derivations and homomorphisms in commutator-simple algebras Alaminos Prats, Jerónimo Brešar, Matej Extremera Lizana, José Castillo Godoy, María Luisa Villena Muñoz, Armando Reyes Derivation Automorphism Antiautomorphism Jordan auto-morphism Local derivation Local automorphism Group algebra The first, third, fourth, and fifth authors were supported by the Grant PID2021-122126NB-C31 funded by MCIN/AEI/ 10.13039/501100011033 and by “ERDF A way of making Europe” and grant FQM-185 funded by Junta de Andalucía. The second author was supported by the Slovenian Research Agency (ARRS) Grant P1-0288. The fourth author was also supported by grant FPU18/00419 funded by MIU. We call an algebra A commutator-simple if [A, A] does not contain nonzero ideals of A. After providing several examples, we show that in these algebras derivations are determined by a condition that is applicable to the study of local derivations. This enables us to prove that every continuous local derivation D : L1(G) → L1(G), where G is a unimodular locally compact group, is a derivation. We also give some remarks on homomorphism-like maps in commutator-simple algebras. 2023-10-27T11:05:33Z 2023-10-27T11:05:33Z 2022-11-20 journal article Published version: Alaminos Prats, J. et al. Derivations and homomorphisms in commutator-simple algebras. Proceedings of the American Mathematical Society 151, 11, 4721-4733. [https://doi.org/10.1090/proc/16483] https://hdl.handle.net/10481/85313 10.1090/proc/16483 eng http://creativecommons.org/licenses/by-nc-nd/4.0/ open access Attribution-NonCommercial-NoDerivatives 4.0 Internacional American Mathematical Society