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DO NOT USE THIS TAG just because your question involves math! If your question is on simplification of a mathematical expression, please ask it at math.stackexchange.com The mathematics tag covers non-applied pure mathematical disciplines that are traditionally not part of the mathematical physics curriculum, such as, e.g., number theory, category theory, algebraic geometry, general topology, algebraic topology, etc.

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A problem with unique decomposition of Galilean transformation

It is very well known that any Galilean transformation on $\mathbb{R}^3\times\mathbb{R}$ can be uniquely written as composition of a maps of the following type: Uniform motion: $(x,t)\to(x+tv,t)\quad …
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