The algebraic and geometric classification of nilpotent Lie triple systems up to dimension four

被引：5

作者：

Abdelwahab, Hani ^{[1
]}

Barreiro, Elisabete ^{[2
]}

Calderon, Antonio J. ^{[3
]}

Fernandez Ouaridi, Amir ^{[2
,3
]}

机构：

[1] Mansoura Univ, Fac Sci, Dept Math, Mansoura, Egypt

[2] Univ Coimbra, Dept Math, CMUC, Apartado 3008, P-3001501 Coimbra, Portugal

[3] Univ Cadiz, Dept Math, Puerto Real, Spain

来源：

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS | 2023年 / 117卷 / 01期

关键词：

Nilpotent Lie triple systems; Algebraic classification; Geometric classification; Annihilator extension; Non-associative triple systems; BINARY-LIE; JORDAN ALGEBRAS; DEGENERATIONS; FIELDS;

D O I：

10.1007/s13398-022-01344-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we generalize the Skjelbred-Sund method, used to classify nilpotent Lie algebras, in order to classify triple systems with non-zero annihilator. We develop this method with the purpose of classifying nilpotent Lie triple systems, obtaining from it the algebraic classification of the nilpotent Lie triple systems up to dimension four. Additionally, we obtain the geometric classification of the variety of nilpotent Lie triple systems up to dimension four.

引用

页数：27

共 43 条

[1] CENTRAL EXTENSIONS OF 4-DIMENSIONAL BINARY LIE ALGEBRAS [J].