Non-Nilpotent Leibniz Algebras with One-Dimensional Derived Subalgebra

Di Bartolo, Alfonso;La Rosa, Gianmarco;Mancini, Manuel
(2024) Mediterranean Journal of Mathematics — Vol. 21, n° 4 (2024)

Files

Non-nilpotent Leibniz algebras with one-dimensional derived subalgebra.pdf
  • Open Access
  • Adobe PDF
  • 377.29 KB
Download

Details

Authors
  • Di Bartolo, AlfonsoUniversità degli Studi di Palermo
    Author
  • La Rosa, GianmarcoUniversità degli Studi di Palermo
    Author
  • Mancini, Manuelorcid-logoUCLouvain
    Author
Abstract
(en) In this paper we study non-nilpotent non-Lie Leibniz F-algebras with one-dimensional derived subalgebra, where F is a field with char(F) different from 2 . We prove that such an algebra is isomorphic to the direct sum of the two-dimensional non-nilpotent non-Lie Leibniz algebra and an abelian algebra. We denote it by L_n , where n=dimL_n. This generalizes the result found in Demir et al. (Algebras and Representation Theory 19:405-417, 2016), which is only valid when F=C. Moreover, we find the Lie algebra of derivations, its Lie group of automorphisms and the Leibniz algebra of biderivations of L_n. Eventually, we solve the coquecigrue problem for L_n by integrating it into a Lie rack.
Affiliations

Citations

  • APA
  • Chicago
  • FWB

Di Bartolo, A., La Rosa, G., & Mancini, M. (2024). Non-Nilpotent Leibniz Algebras with One-Dimensional Derived Subalgebra. Mediterranean Journal of Mathematics, 21(4). https://doi.org/10.1007/s00009-024-02679-0 (Original work published 2024)