Locally Operating Realizations of Transformation Lie Groups

May, 1985
46 pages
Published in:
  • J.Math.Phys. 26 (1985) 2096
Report number:
  • DFTUZ-85-5

Citations per year

1993199720012005200910
Abstract: (AIP)
Using the Mackey theory of induced representations, a systematic study of the locally operating multiplier realizations of a connected Lie groupG that acts transitively on a space‐time manifold is presented. We obtain a mathematical characterization of the locally operating multiplier realizations and a reduction of the problem of multiplier locally operating realizations to linear ones via a splitting group G‘;m for G. In this way the locally operating multiplier realizations are obtained by induction from finite‐dimensional linear representations of a well‐determined subgroup of Ḡ. Some examples, such as the two‐dimensional Euclidean group, the Galilei group, and the one‐dimensional Newton–Hooke group, are given.