Journal of Nonlinear Mathematical Physics

Volume 1, Issue 3, August 1994, Pages 295 - 308

On Linear and Non-Linear Representations of the Generalized Poincaré Groups in the Class of Lie Vector Fields

Authors
Wilhelm Fushchych, Renat Zhdanov, Victor Lahno
Corresponding Author
Wilhelm Fushchych
Received 18 April 1994, Available Online 1 August 1994.
DOI
10.2991/jnmp.1994.1.3.4How to use a DOI?
Abstract

We study representations of the generalized Poincaré group and its extensions in the class of Lie vector fields acting in a space of n + m independent and one dependent variables. We prove that an arbitrary representation of the group P(n, m) with max {n, m} 3 is equivalent to the standard one, while the conformal group C (n, m) has non-trivial nonlinear representations. Besides that, we investigate in detail representations of the Poincaré group P (2, 2), extended Poincaré groups P (1, 2), P (2, 2), and conformal groups C (1, 2), C (2, 2) and obtain their linear and nonlinear representations.

Copyright
© 2006, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
1 - 3
Pages
295 - 308
Publication Date
1994/08/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.2991/jnmp.1994.1.3.4How to use a DOI?
Copyright
© 2006, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - Wilhelm Fushchych
AU  - Renat Zhdanov
AU  - Victor Lahno
PY  - 1994
DA  - 1994/08/01
TI  - On Linear and Non-Linear Representations of the Generalized Poincaré Groups in the Class of Lie Vector Fields
JO  - Journal of Nonlinear Mathematical Physics
SP  - 295
EP  - 308
VL  - 1
IS  - 3
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.1994.1.3.4
DO  - 10.2991/jnmp.1994.1.3.4
ID  - Fushchych1994
ER  -