Article Sidebar

Untitled
Date Published: 30/09/2020
Online Published: 30/09/2020
Abstract Views: 108
Views Untitled: 70
DOI: https://doi.org/10.54607/hcmue.js.17.9.2816(2020)
Issue
Vol. 17 No. 9 (2020)
Section
Articles
How to Cite
Nguyễn , T. C. T. (2020). A SUBCLASS OF 7-DIMENSIONAL SOLVABLE LIE ALGEBRAS HAVING 5-DIMENSIONAL NILRADICALS AND ITS REPRESENTATIONS. HCMUE Journal of Science, 17(9), 1565. https://doi.org/10.54607/hcmue.js.17.9.2816(2020)

A SUBCLASS OF 7-DIMENSIONAL SOLVABLE LIE ALGEBRAS HAVING 5-DIMENSIONAL NILRADICALS AND ITS REPRESENTATIONS

Thị Cẩm Tú Nguyễn

Main Article Content

Abstract

 

          The paper is to classify seven-dimensional solvable Lie algebras that have the five-dimensional nilpotent Lie algebras as their nilradical. All seven-dimensional indecomposable solvable Lie algebras with a given nilradical are constructed. This result contributes to the complete classification of the class of seven-dimensional real solvable Lie algebras which are presently unsolved. Moreover, the adjoint and co-adjoint representations of these algebras are also described in this paper. These are two extremely important representations in the representation theory of Lie algebras. As a consequence, a clearer understanding of the newly constructed Lie algebras is formed.

 

Keywords

Lie algebras, Solvable Lie algebras, Nilradical, Representation

Article Details

References

Cartan, E. (1894). Sur la structure des groupes de transformations finis et continus. Thèse. Nony, Paris.
Dixmier, J. (1958). Sur les represéntations unitaires des groupes de Lie nilpotents III. Canad. J. Math, 321-348.
Hindeleh, & Thompson (2008). Seven dimensional Lie algebras with a fourdimensional nilradical. Algebras, Groups, and Geometries, 243-265.
Gantmacher, F. R. (1939). On the classification of real simple Lie groups. Sb. Math, 217-250.
Gong, M. P. (1998). Classification of Nilpotent Lie algebras of Dimension 7 (Over Algebraically Closed Fields and R). PhD. Thesis. University of Waterloo, Ontario, Canada.
Levi, E. E. (1905). Sulla struttura dei gruppi finiti e continui. Atti Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur, 551-565.
Malcev, A. I. (1945). On solvable Lie algebras. Izv. Ross. Akad. Nauk Ser. Mat, 329-356.
Mubarakzyanov, G. (1963). Classification of solvable Lie algebras of dimension 6 with one nonnilpotent basis element. Izv. Vyssh Uchebn. Zaved. Mat, 104-116.
Mubarakzyanov, G. (1966). Some theorems on solvable Lie algebras. Izv. Vyssh. Uchebn. Zaved. Mat, 95-98.
Parry, A. R. (2007). A classification of real indecomposable solvable Lie algebras of small dimension with codimension one nilradicals. Master Thesis. Utah State University, Logan, Utah.
Safiulina, E. (1964). Classification of nilpotent Lie algebras of dimension seven. Math. Methods Phys. Izd. Kazan. Univ, 66-69.
Tsagas, G. (1999). Classification of nilpotent Lie algebras of dimension eight. J. Inst. Math. Comput. Sci. Math. Ser, 179-183.
Turkowski, R. (1990). Solvable Lie algebras of dimension six. J. Math. Phys, 1344-1350.