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1 Form and symmetries
2 Our solution
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is not a base form

1 Form and symmetries

Notice that symmetries form a Lie superalgebra:

if 

and

then 

This superalgebra acts on .

However, it turns out that is not a base form with respect to symmetries. More precisely:

is invariant but not horizontal

Therefore we cannot integrate over cycles in the base:

does not descend to a PDF on the coset  

2 Our solution

We factorize over symmetries, but not over all symmetries. We will identify a subgroup in the group of symmeties, which has the properties:

  • It is large enough for the factorspace to have interesting integration cycles.

  • It is small enough to allow us to define a closed base PDF which we will call .

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