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

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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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  -