Sheaf representations and graded manifolds

Abstract

AbstractThe sheaf representation theory of Mulvey extends to Z2-graded-commutative Gelfand rings. On application to Kostant's theory of graded manifolds (X, A), for which partitions of unity are known to exist, this gives a canonical way of constructing the sheaf A from the Gelfand algebra A(X). A direct definition of a product graded manifold is possible using coalgebraic completion of the tensor products A(U)⊗B(V). By using this completion of the tensor product, graded Lie groups may be discussed without further use of coalgebras. Graded Lie groups are necessarily globally trivial and the structure maps are derived