Classification of Symmetry Lie Algebras of the Canonical Geodesic Equations of Five-Dimensional Solvable Lie Algebras

被引：6

作者：

Almusawa, Hassan ^{[1
,2
]}

Ghanam, Ryad ^{[3
]}

Thompson, Gerard ^{[4
]}

机构：

[1] Virginia Commonwealth Univ, Dept Math & Appl Math, Richmond, VA 23284 USA

[2] Jazan Univ, Coll Sci, Dept Math, Jazan 45142, Saudi Arabia

[3] Virginia Commonwealth Univ Qatar, Dept Liberal Arts & Sci, Doha 8095, Qatar

[4] Univ Toledo, Dept Math, Toledo, OH 43606 USA

来源：

SYMMETRY-BASEL | 2019年 / 11卷 / 11期

关键词：

symmetry algebra; Lie group; canonical connection; system of geodesic equations; INVERSE PROBLEM;

D O I：

10.3390/sym11111354

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

In this investigation, we present symmetry algebras of the canonical geodesic equations of the indecomposable solvable Lie groups of dimension five, confined to algebras A(5,7)(abc) to A(18)(a). For each algebra, the related system of geodesics is provided. Moreover, a basis for the associated Lie algebra of the symmetry vector fields, as well as the corresponding nonzero brackets, are constructed and categorized.

引用

页数：30

共 50 条

[1] Five-dimensional paracontact Lie algebras
Calvaruso, Giovanni
Perrone, Antonella
[J]. DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 2016, 45 : 115 - 129
[2] ON PARASASAKIAN STRUCTURES ON FIVE-DIMENSIONAL LIE ALGEBRAS
Smolentsev, N. K.
Shagabudinova, I. Y.
[J]. VESTNIK TOMSKOGO GOSUDARSTVENNOGO UNIVERSITETA-MATEMATIKA I MEKHANIKA-TOMSK STATE UNIVERSITY JOURNAL OF MATHEMATICS AND MECHANICS, 2021, (69): : 37 - 52
[3] Classification of solvable Lie algebras
de Graaf, WA
[J]. EXPERIMENTAL MATHEMATICS, 2005, 14 (01) : 15 - 25
[4] Five-dimensional K-contact Lie algebras
Calvaruso, Giovanni
Fino, Anna
[J]. MONATSHEFTE FUR MATHEMATIK, 2012, 167 (01): : 35 - 59
[5] Five-dimensional K-contact Lie algebras
Giovanni Calvaruso
Anna Fino
[J]. Monatshefte für Mathematik, 2012, 167 : 35 - 59
[6] Six-Dimensional Lie Algebras with a Five-Dimensional Nilradical
Shabanskaya, Anastasia
Thompson, Gerard
[J]. JOURNAL OF LIE THEORY, 2013, 23 (02) : 313 - 355
[7] On the Symmetries of Five-Dimensional Solvable Lie Groups
Mostefaoui, Assia
Belarbi, Lakehal
[J]. JOURNAL OF LIE THEORY, 2020, 30 (01) : 155 - 169
[8] CLASSIFICATION OF FILIFORM SOLVABLE LIE-ALGEBRAS
SUND, T
[J]. COMMUNICATIONS IN ALGEBRA, 1994, 22 (11) : 4303 - 4359
[9] CLASSIFICATION OF FILIFORM SOLVABLE LIE-ALGEBRAS
SUND, T
[J]. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1993, 317 (02): : 145 - 148
[10] Quivers and Three Dimensional Solvable Lie Algebras
Pike, Jeffrey
[J]. JOURNAL OF LIE THEORY, 2017, 27 (03) : 707 - 726

← 1 2 3 4 5 →