Lagrangian extensions and left-symmetric structures on the four-dimensional real Lie superalgebras

Authors

  • Sofiane Bouarroudj Division of Science and Mathematics, New York University Abu Dhabi, Abu Dhabi, United Arab Emirates
  • Ana-Maria Radu Division of Science and Mathematics, New York University Abu Dhabi, Abu Dhabi, United Arab Emirates

DOI:

https://doi.org/10.3842/umzh.v78i9-10.9648

Keywords:

Lagrangian extension, left-symmetric structures, Novikov structures, Balinsky-Novikov structures, Quasi-Frobenius Lie superalgebras

Abstract

UDC 512.81; 512.55

Over real numbers, Backhouse classified all four-dimensional Lie superalgebras. From this list, we  investigate the Lie superalgebras that can be obtained as Lagrangian extensions. Moreover, we study left-symmetric structures on these Lie superalgebras. Furthermore, except two of them, we show that they are all Novikov superalgebras.

References

The full version of this paper will be published in Ukrainian Mathematical Journal, Vol. 78, No. 9-10, 2026.

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Published

19.09.2026

Issue

Vol. 78 No. 9-10 (2026)

Section

Research articles