Cocycle in

Step 1: construct an element of

Consider an element of corresponding
to the extension:

(Remember that is defined in Eq. (15).)

Step 2: compose it with an intertwiner

There exists a -invariant map

Composing it with the element of 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:

In particular, take — the algebra of supermatrices. Let us view the exterior product as a subspace in .

For any element we define:

It defines a map:

Description of the intertwiner

For and belonging to , we define: