Cocycle in 
Step 1: construct an element of 
Consider an element of corresponding
to the extension:
corresponding
to the extension:
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(Remember that 
is defined in Eq. (15).)
is defined in Eq. (15).)Step 2: compose it with an intertwiner 
There exists a 
-invariant map
-invariant map
Composing it with the element of we
get a class in 
.
we
get a class in .We will now describe this intertwiner.
Construction of the intertwiner of Eq. (19)
Intertwiner: algebraic preliminaries
Suppose that we have an associative algebra 
. For any 
consider their product:
. For any consider their product:
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In particular, take 
— the algebra of supermatrices. Let us view the exterior product 
as a subspace in 
.
— the algebra of supermatrices. Let us view the exterior product as a subspace in .For any element 
we define:
we define:
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It defines a map:
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Description of the intertwiner
For 
and 
belonging to , we define:
and belonging to , we define:
