Equivariant Ω

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Equivariant

Let us assume that the symmetries defined in Eq. (2) form a closed algebra. It is parametrized by

and

We have the following Cartan form:

(4)

This is always true to the first order in

and

. For this to be true to all orders in

and

, we need:

(5)

(6)

Let us summarize the derivation. We have:
Therefore:
(7)
(8)
In passing from (7) to (8) we assumed that both and preserve the measure of integration .
The last line coincides with Eq. (3).

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