On solvable Lie superalgebras of maximal rank

2024/02/18 by B. A. Omirov, Omirov, Bakhrom A., I. S. Rakhimov +3
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2402.11479

openalex publication_date 2024/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we establish some basic properties of superderivations of Lie superalgebras. Under certain conditions, for solvable Lie superalgebras with given nilradicals, we give estimates for upper bounds to dimensions of complementary subspaces to the nilradicals. Moreover, under these conditions we describe the solvable Lie superalgebras of maximal rank. Namely, we prove that an arbitrary solvable Lie superalgebra of maximal rank is isomorphic to the maximal solvable extension of nilradical of maximal rank.

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