Surveys in Differential Geometry
Volume 15 (2010)
Automorphisms of graded super symplectic manifolds
Pages: 237 – 254
In section 1 we present the language of differential analysis in graded locally convex infinite dimensional vector spaces that was studied in . In section 2 we give results on diffeological Lie groups and Lie algebras and formulate diffeological versions of the fundamental theorems of Lie. In section 3 we introduce the notion of graded supermanifolds and we indicate a method of constructing non-trivial compact graded supermanifolds with non-degenerate graded differential forms which generalize symplectic and contact structures to the graded case. In section 4 we study automorphisms of generalizations of some of the classical geometric structures to compact graded supermanifold, M, and show that these automorphism groups are diffeological Lie subgroups of the Lie group of superdiffeomorphisms of M.