Cartan Algebra Research Articles

The Cartan algebra of exterior differential forms as a supermanifold: morphisms and manifolds associated with them

Abstract A supermanifold, M m n , can be caracterired by its smooth superfunctions which constitute an algebra A (Leites, Kostant). We associate canonically ⪡a la Gelfand⪢ certain fibred manifolds on which the automorphisms (the Jordan automorphisms) of A act as diffeomorphisms. For example, the kernels of all homomorphisms from the algebra of superfunctions onto the Grassmann algebra of dimension n form naturally a manifold of dimension m2n-1 if n is even. To be more specific we explain this and similar constructions in the case of the algebra of smooth exterior differential forms defined on a smooth manifold. This algebra defines a particular supermanifold Mm/m.