Locally Operating Realizations of Transformation Lie Groups
May, 198546 pages
Published in:
- J.Math.Phys. 26 (1985) 2096
DOI:
Report number:
- DFTUZ-85-5
Citations per year
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.References(27)
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