On linear and non-linear representations of the generalized poincar´e groups in the class of lie vector fields

Abstract

We study representations of the generalized Poincar´e 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 Poincar´e group P (2, 2), extended Poincar´e groups e P (1, 2), e P (2, 2), and conformal groups C (1, 2), C (2, 2) and obtain their linear and nonlinear representations. © 1994 by Mathematical Ukraina Publisher.