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Classification of linear representations of the Galilei, Poincaré, and conformal algebras in the case of a two-dimensional vector field and their applications

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Abstract

We present the classification of linear representations of the Galilei, Poincaré, and conformal algebras nonequivalent under linear transformations in the case of a two-dimensional vector field. The obtained results are applied to the investigation of the symmetry properties of systems of nonlinear parabolic and hyperbolic equations.

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Authors and Affiliations

  1. Poltava State Technical University, Poltava

    M. I. Serov, T. O. Zhadan & L. M. Blazhko

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  1. M. I. Serov
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  2. T. O. Zhadan
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  3. L. M. Blazhko
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 8, pp. 1128–1145, August, 2006.

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Serov, M.I., Zhadan, T.O. & Blazhko, L.M. Classification of linear representations of the Galilei, Poincaré, and conformal algebras in the case of a two-dimensional vector field and their applications. Ukr Math J 58, 1275–1297 (2006). https://doi.org/10.1007/s11253-006-0133-2

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  • DOI: https://doi.org/10.1007/s11253-006-0133-2

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