2021/11/01 by Sofiane Bouarroudj, Bouarroudj, Sofiane, Yoshiaki Maeda +1 · 2 citations
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2111.00838
openalex publication_date 2021/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.