Matrix representations of third order jet groups

Dusan Navratil

Abstract


In this paper, faithful matrix representations of the jet groups \(G^3_n\) are presented, following a detailed description of their components in block form. Such  groups can be used further to study symmetries of differential equations. Elements of these matrix representations are derived.

Keywords


Jet group; matrix; representation

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References


Burianek, M., Invariants of Jet Groups and Applications in Continuum Mechanics, Bachelor Thesis (in Czech), Brno University of Technology, Brno, 2020.

Kolar, I., Michor, P., Slovak J., Natural Operations in Differential Geometry, Springer, Berlin, 1993.

Kures, M., On Coordinate Expressions of Jet Groups and Their Representations, in: Proceedings of the Twenty-Second International Conference on Geometry, Integrability and Quantization, Vol. 22 (2021), 142–254, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences.

Olver, P., Equivalence, Invariants and Symmetry, Cambridge University Press, Cambridge, 1995.

Saunders, D. J., The Geometry of Jet Bundles, Cambridge University Press, Cambridge, 1989.




DOI: http://dx.doi.org/10.17951/a.2022.76.1.47-59
Date of publication: 2022-10-05 20:39:34
Date of submission: 2022-10-04 21:10:46


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