On the classification of 2-solvable Frobenius Lie algebras

Autor:	Diatta, Andre, Manga, Bakary, Mbaye, Ameth
Rok vydání:	2022
Předmět:	Mathematics - Differential Geometry Mathematical Physics Mathematics - Commutative Algebra Mathematics - Symplectic Geometry 17B05 17B08 15A27 53A15 53D15 22E60 17B60 70G45 16W25 13B25
Zdroj:	Journal of Lie Theory 33 (2023), No. 3, 799-830
Druh dokumentu:	Working Paper
Popis:	We discuss the classification of 2-solvable Frobenius Lie algebras. We prove that every 2-solvable Frobenius Lie algebra splits as a semidirect sum of an n-dimensional vector space V and an n-dimensional maximal Abelian subalgebra (MASA) of the full space of endomorphisms of V. We supply a complete classification of 2-solvable Frobenius Lie algebras corresponding to nonderogatory endomorphisms, as well as those given by maximal Abelian nilpotent subalgebras (MANS) of class 2, hence of Kravchuk signature (n-1,0,1). In low dimensions, we classify all 2-solvable Frobenius Lie algebras in general up to dimension 8. We correct and complete the classification list of MASAs of sl(4, R) by Winternitz and Zassenhaus. As a biproduct, we give a simple proof that every nonderogatory endormorphism of a real vector space admits a Jordan form and also provide a new characterization of Cartan subalgebras of sl(n, R). Comment: V3: 26 pages, Latex. A few misprints corrected. To appear at Journal of Lie Theory
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2209.05595 Zobrazit plný text záznamu View this record from Arxiv