Left-symmetric superalgebras and Lagrangian extensions of Lie superalgebras in characteristic 2

2025/01/26 by Benayadi, Saïd, Bouarroudj, Sofiane, Ehret, Quentin · 3 citations
#17B05 #17B50 #17B56 #17D25 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2501.15432

Abstract

The purpose of this paper is twofold. First, we introduce the notions of left-symmetric and left alternative structures on superspaces in characteristic 2. We describe their main properties and classify them in dimension 2. We show that left-symmetric structures can be queerified if and only if they are left-alternative. Secondly, we present a method of Lagrangian extension of Lie superalgebras in characteristic 2 with a flat torsion-free connection. We show that any strongly polarized quasi-Frobenius Lie superalgebra can be obtained as a Lagrangian extension. Further, we demonstrate that Lagrangian extensions are classified by a certain cohomology space that we introduce. To illustrate our constructions, all Lagrangian extensions in dimension 4 have been described.

Cited by

• On Poisson superalgebras in characteristic 2
• Flat quasi-Frobenius Lie superalgebras
• Jacobson identities for post-Lie algebras in positive characteristic

Related

• Lagrangian extensions and left symmetric structures on the four-dimensional real Lie superalgebras
• Double and Lagrangian extensions for quasi-Frobenius Lie superalgebras
• Support varieties for Lie superalgebras in characteristic 2
• Left-symmetric Structures on Complex Simple Lie Superalgebras
• Superalgebras with Homogeneous structures of Lie type