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Extensions of Realisations for Low-Dimensional Lie Algebras

by Iryna Yehorchenko

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Submission summary

Authors (as registered SciPost users): Iryna Yehorchenko
Submission information
Preprint Link: scipost_202212_00054v2  (pdf)
Date accepted: 2023-08-30
Date submitted: 2023-06-19 02:51
Submitted by: Yehorchenko, Iryna
Submitted to: SciPost Physics Proceedings
Proceedings issue: 34th International Colloquium on Group Theoretical Methods in Physics (GROUP2022)
Ontological classification
Academic field: Physics
  • Mathematical Physics
Approach: Theoretical


We find extensions of realisations of some low-dimensional Lie algebras, in particular, for the Poincar\'e algebra for one space dimension. Using inequivalent extensions, we performed a comprehensive classification of relative differential invariants for these Lie algebras. We show the difference between the classification of extensions of realisations, and the classification of nonlinear realisations of Lie algebras.

Published as SciPost Phys. Proc. 14, 048 (2023)

Author comments upon resubmission

I have taken into account all the reviewer's comments and made the requested changes. I added more information on applications of relative differential invariants in mathematics and physics, and clarified which new and original results are presented in this paper. Definition 4 was clarified to avoid the impression of a circular definition. Examples and calculations in the paper are new results that was pointed out.

List of changes

1. New text of the Abstract.
2. Rewritten Introduction, including reformulation of Definition 4.
3. Added reference 3
4. Corrected mistake in line 4, column 4, Table 1 (page 4)
5. Rewritten Conclusions.
6. Changed the order of references in accordance with the rewritten introduction
7. Calculations in Section 3 on page 4 were abridged to leave space for extended motivation and application comments.

Submission & Refereeing History

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Resubmission scipost_202212_00054v2 on 19 June 2023

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