This question is a follow-up to a previous question. In this survey of Symplectic Geometry by Arnol'd and Givental, the example of a constant-speed moving particle considered in the previous question was briefly mentioned on Page 62 as follows:
The action of the group by left translations on its cotangent bundle is Poisson. The corresponding momentum mapping P:T∗G→g∗ coincides with the right translation of covectors to the identity element of the group.
We can take G=R to reduce to our example. Then T∗G≅R2, g∗≅R, and the identity element of the group R is zero.
How does the momentum mapping P:R2→R coincide with the right translation of covectors to zero?
So I'm asking what exactly the map P is and what Arnol'd and Givental mean by "the right translation of covectors to zero".
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