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A Lie algebra $L$ is called 2-step nilpotent if $L$ is not abelian and $[L, L]$ lies in the center of $L$ . 2-step nilpotent Lie algebras are useful in the study of some geometric problems, and their classification has been an important problem in Lie theory. In this paper, we give a classification of 2-step nilpotent Lie algebras of dimension 9 with 2-dimensional center.

Classification of 4-dimensional nilpotent complex Leibniz algebras.

Sergio Albeverio, Bakhrom A. Omirov, Isamiddin S. Rakhimov (2006)

Extracta Mathematicae

Classification of all associative mono- $n$ -ary algebras with 2 elements.

Andres, Stephan Dominique (2009)

International Journal of Mathematics and Mathematical Sciences

Classification of filiform Lie algebras in dimension 8.

José María Ancochea Bermúdez, Michel Goze (1986)

Extracta Mathematicae

Classification of finite dimensional modular Lie superalgebras with indecomposable Cartan matrix.

Bouarroudj, Sofiane, Grozman, Pavel, Leites, Dimitry (2009)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Classification of Harish-Chandra modules over the Virasoro Lie algebra.

Olivier Mathieu (1992)

Inventiones mathematicae

Classification of irreducible weight modules

Olivier Mathieu (2000)

Annales de l'institut Fourier

Let $𝔤$ be a reductive Lie algebra and let $𝔥$ be a Cartan subalgebra. A $𝔤$ -module $M$ is called a weighted module if and only if $M = \oplus_{λ} M_{λ}$ , where each weight space $M_{λ}$ is finite dimensional. The main result of the paper is the classification of all simple weight $𝔤$ -modules. Further, we show that their characters can be deduced from characters of simple modules in category $𝒪$ .

Classification of JBW*-triples of Type I.

Günther Horn (1987)

Mathematische Zeitschrift

Classification of Loop Modules with finite dimensional weight spaces.

S. Eswara Rao (1996)

Mathematische Annalen

Classification of p-adic 6-dimensional filiform Leibniz algebras by solutions of x q = a

Manuel Ladra, Bakhrom Omirov, Utkir Rozikov (2013)

Open Mathematics

We study the p-adic equation x q = a over the field of p-adic numbers. We construct an algorithm which gives a solvability criteria in the case of q = p m and present a computer program to compute the criteria for any fixed value of m ≤ p − 1. Moreover, using this solvability criteria for q = 2; 3; 4; 5; 6, we classify p-adic 6-dimensional filiform Leibniz algebras.

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Displaying 41 – 60 of 173

Charakterisierung symmetrischer R-Räume durch ihre Einheitsgitter.

Chevalley-Jordan decomposition for a class of locally finite Lie algebras

Classes of Lie algebras and Cartan subalgebras.

Classical $R$ -operators and integrable generalizations of Thirring equations.

Classification des algèbres de Lie filtrées

Classification des algèbres de Lie graduées simples de croissance ... 1.

Classification des algèbres de Lie simples

Classification of 2-step nilpotent Lie algebras of dimension 9 with 2-dimensional center