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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 66 | Issue 10 | Year 2020 | Article Id. IJMTT-V66I10P511 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I10P511

OBSERVING REPRESENTATIONS OF THE LIE GROUP SL(3, R) FROM VANTAGE POINT OF SYMMETRIES OF SECOND ORDER LINEAR O.D.E’s


Uchechukwu Opara
Abstract

An in-depth view of the reducibility properties of second order linear O.D.E’s also offers a unique setting to draw up links between representations of the admitted symmetry group SL(3, R). These links are exposed in this article, with further elements of symmetry methods for differential equations and abstract group algebra also elucidated.

Keywords
Kummer-Liouville point transform, Lie group representations and isomorphisms, Projective special linear group, Semiinvariants of second order linear O.D.E’s .
References

[1] U. Opara , \On the Eight Dimensional Point Symmetries of Second Order Linear O.D.E's" in Journal of Generalized Lie Theory and Applications 14(2020): 297. doi:10.37421/GLTA.2020.14.297 .
[2] P. E. Hydon , Symmetry Methods for Differential Equations- A Beginner's Guide, Cambridge University Press, 2000
[3] P. J. Olver , Applications of Lie Groups to Differential Equations, 2nd edition, Springer-Verlag, 1993 .
[4] L. M. Berkovich and N. H. Rozov, \ Transformation of Linear Differential Equations of Second Order and Adjoined Nonlinear Equations" in Archivum Mathematicum, copyright Masaryk University, Czech Republic, Vol. 33, No. 1-2, 1997, pp. 75-98 .
[5] H. Stephani and M. Maccallum, - Differential Equations: Their Solution Using Symmetries, Cambridge University Press, 1989 .

Citation :

Uchechukwu Opara, "OBSERVING REPRESENTATIONS OF THE LIE GROUP SL(3, R) FROM VANTAGE POINT OF SYMMETRIES OF SECOND ORDER LINEAR O.D.E’s," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 10, pp. 70-75, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I10P511

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