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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Derivations and homomorphisms in commutator-simple algebras
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by J. Alaminos, M. Brešar, J. Extremera, M. L. C. Godoy and A. R. Villena
Proc. Amer. Math. Soc. 151 (2023), 4721-4733
DOI: https://doi.org/10.1090/proc/16483
Published electronically: August 4, 2023

Abstract:

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 $D\colon L^1(G)\to L^1(G)$, where $G$ is a unimodular locally compact group, is a derivation. We also give some remarks on homomorphism-like maps in commutator-simple algebras.
References
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Bibliographic Information
  • J. Alaminos
  • Affiliation: Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, Granada, Spain
  • MR Author ID: 641559
  • ORCID: 0000-0002-7857-7833
  • Email: alaminos@ugr.es
  • M. Brešar
  • Affiliation: Faculty of Mathematics and Physics, University of Ljubljana, and Faculty of Natural Sciences and Mathematics, University of Maribor, Slovenia
  • ORCID: 0000-0001-7574-212X
  • Email: matej.bresar@fmf.uni-lj.si
  • J. Extremera
  • Affiliation: Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, Granada, Spain
  • MR Author ID: 692437
  • Email: jlizana@ugr.es
  • M. L. C. Godoy
  • Affiliation: Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, Granada, Spain
  • MR Author ID: 1306099
  • ORCID: 0000-0001-5772-5385
  • Email: mgodoy@ugr.es
  • A. R. Villena
  • Affiliation: Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, Granada, Spain
  • MR Author ID: 309482
  • Email: avillena@ugr.es
  • Received by editor(s): October 25, 2022
  • Received by editor(s) in revised form: March 10, 2023
  • Published electronically: August 4, 2023
  • Additional Notes: 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
  • Communicated by: Javad Mashreghi
  • © Copyright 2023 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 151 (2023), 4721-4733
  • MSC (2020): Primary 43A20, 47L10, 16W20, 16W25
  • DOI: https://doi.org/10.1090/proc/16483
  • MathSciNet review: 4634876