Current Hom-Lie algebras

Authors

  • Torkia Ben Jmaa University of Gabes
  • Abdenacer Makhlouf University of Haute Alsace, Mulhouse
  • Nejib Saadaoui University of Gabes

DOI:

https://doi.org/10.12697/ACUTM.2022.26.08

Keywords:

Current Hom-Lie algebra, representation, current Heisenberg Hom-Lie algebra, derivation, cohomology, extension

Abstract

In this paper, we study Hom-Lie structures on tensor products. In particular, we consider current Hom-Lie algebras and discuss their representations. We determine faithful representations of minimal dimension of current Heisenberg Hom-Lie algebras. Moreover derivations, including generalized derivations, and centroids are studied. Furthermore, cohomology and extensions of current Hom-Lie algebras are also considered.

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Author Biographies

Torkia Ben Jmaa, University of Gabes

PhD Student, Deprtment of Mathematics 

Abdenacer Makhlouf, University of Haute Alsace, Mulhouse

Professor 

Head of Mathematics Department 

Deputy Director of Institute of Informatics, Mathematics, Automation and Signal

Vice-President delegate to Equity and Diversity  

Nejib Saadaoui, University of Gabes

Assistant Professor  

Institut Supérieur d'Informatique de Medenine. 

 

 

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Published

2022-05-30

Issue

Vol. 26 No. 1 (2022)

Section

Articles