The purpose of this work is to study Lie superalgebroid structures on the space of superdifferential -forms over the supermanifolds whose superfunctions are the differential forms on its underlying manifold. These superalgbroids are constructed from graded Poisson structures defined on the latter superalgebra.
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3 results for “superdifferentials”
Establishes a Lorentzian Lasry-Lions regularization theorem for functions on globally hyperbolic spacetimes.
problem Optimal transport with regularizing pairs
method Local semiconcavity and future-directed timelike superdifferentials
result Derives regularizing pairs for optimal transport under general assumptions
We describe explicitly Lie superalgebra isomorphisms between the Lie superalgebras of first-order superdifferential operators on supermanifolds, showing in particular that any such isomorphism induces a diffeomorphism of the supermanifolds. We also prove that the group of automorphisms of such a Lie superalgebra is a s…