Derivations and homomorphisms in commutator-simple algebras
Metadatos
Mostrar el registro completo del ítemAutor
Alaminos Prats, Jerónimo; Brešar, Matej; Extremera Lizana, José; Castillo Godoy, María Luisa; Villena Muñoz, Armando ReyesEditorial
American Mathematical Society
Materia
Derivation Automorphism Antiautomorphism Jordan auto-morphism Local derivation Local automorphism Group algebra
Fecha
2022-11-20Referencia bibliográfica
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]
Patrocinador
MCIN/AEI/ 10.13039/50110001103 Grant PID2021-122126NB-C31; “ERDF A way of making Europe”; Junta de Andalucía FQM-185; Slovenian Research Agency (ARRS) Grant P1-0288; MIU: FPU18/00419Resumen
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.