Double and Lagrangian extensions for quasi-Frobenius Lie superalgebras

Sofiane Bouarroudj, Yoshiaki Maeda

Research output: Contribution to journalArticlepeer-review


A Lie superalgebra is called quasi-Frobenius if it admits a closed anti-symmetric non-degenerate bilinear form. We study the notion of double extensions of quasi-Frobenius Lie superalgebra when the form is either orthosymplectic or periplectic. We show that every quasi-Frobenius Lie superalgebra that satisfies certain conditions can be obtained as a double extension of a smaller quasi-Frobenius Lie superalgebra. We classify all 4-dimensional quasi-Frobenius Lie superalgebras, and show that such Lie superalgebras must be solvable. We study the notion of T∗-extensions (or Lagrangian extensions) of Lie superalgebras, and show that they are classified by a certain cohomology space we introduce. Several examples are provided to illustrate our construction.

Original languageEnglish (US)
Article number2450001
JournalJournal of Algebra and Its Applications
StateAccepted/In press - 2022


  • double extension
  • orthosymplectic and periplectic forms
  • Quasi-Frobenius Lie superalgebra
  • T-extension

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Applied Mathematics


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