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Equivalence of Vector Field Realizations of Lie Algebras from the Lie Group Point of View

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Book cover Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 1 (LT-XII/QTS-X 2017)

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Abstract

The equivalence of vector field realizations of Lie algebras is considered from the viewpoint of the Lie algebra and also from the corresponding (local) Lie group. It is shown that for some stages in the establishment of the equivalence things are simpler in the case of the Lie group. A lemma about the equivalence of the sum of realizations is proposed.

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References

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Acknowledgements

MN is grateful for the hospitality extended to her at the Department of mathematics, FNSPE, Czech Technical University in Prague, where part of this work was done. SP is grateful for the hospitality extended to him at the Institute of Mathematics of NAS of Ukraine.

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Authors and Affiliations

  1. Institute of Mathematics of NAS of Ukraine, 3 Tereshchenkivska Str., Kyiv, 01004, Ukraine

    Maryna Nesterenko

  2. Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Trojanova 13, 120 00, Prague, Czech Republic

    Severin Pošta

Authors
  1. Maryna Nesterenko
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  2. Severin Pošta
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Correspondence to Severin Pošta .

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Editors and Affiliations

  1. Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Vladimir Dobrev

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Nesterenko, M., Pošta, S. (2018). Equivalence of Vector Field Realizations of Lie Algebras from the Lie Group Point of View. In: Dobrev, V. (eds) Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 1 . LT-XII/QTS-X 2017. Springer Proceedings in Mathematics & Statistics, vol 263. Springer, Singapore. https://doi.org/10.1007/978-981-13-2715-5_30

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