Algebraic Interpretation
1 Wavy superalgebra and BV algebra
Let us consider a BV algebra 
with the generator 
. Let 
be the Lie
superalgebra which is obtained from by forgetting the associative
algebra structure and flipping parity, and 
the corresponding
wavy Lie superalgebra.
We need to flip parity in order to turn
into a Lie superalgebra operation. If the parity of
as an element of
, is
, then the parities of the corresponding elements of
are:
and
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We have to check that:
2 Form 
as an intertwiner
Let us consider the particular case when is the algebra of functions
on the odd symplectic manifold 
.
In this case, naturally acts on the differential forms on 
. Indeed, every
element 
determines the corresponding right-invariant vector
field on . Then 
would act as a Lie derivative along this vector field,
and 
acts as a contraction.
We can
consider 
as a linear map from 
to the space of differential forms on ;
for each 
, this map computes 
— is an
intertwiner:
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