Generalized forms and vector fields

Abstract

The generalized vector is defined on an n-dimensional manifold. The interior product and Lie derivative acting on generalized p-forms, −1 ≤ p ≤ n are introduced. The generalized commutator of two generalized vectors is defined. Adding a correction term to Cartan's formula, the generalized Lie derivative's action on a generalized vector field is defined. We explore various identities of the generalized Lie derivative with respect to generalized vector fields, and discuss an application.