Another term for dg-manifold .
An N-[supermanifold] is a supermanifold equipped with a lift of the -grading to a -grading through the standard homomorphism .
A Q-[supermanifold] is a supermanifold equipped with an odd-graded vector field (i.e. an odd-graded derivation of the algebra of functions) which is homological, i.e. the super Lie bracket with itself vanishes: .
A P-[supermanifold] is a supermanifold equipped with a graded symplectic structure.
It is an old observation by Maxim Kontsevich, amplified by Pavol Severa (ref…) that NQ-supermanifolds are precisely those supermanifolds which are equipped with an action of , the endomorphism monoid of the odd line.
NQ-supermanifolds are an equivalent way of thinking of ∞-Lie algebroids. See the list of references there.
NQP-supermanifolds are hence symplectic Lie n-algebroids
The “Q-manifold”-terminology is due to