Differential Forms, Hopf Algebra and General Relativity I

Abstract

We review the language of differential forms and their applications to Riemannian Geometry with an orientation to General Relativity. Working with the principal algebraic and differential operations on forms, we obtain the structure equations and their symmetries in terms of a new product (the co-multiplication). It is showen how the Cartan - Grassmann algebra can be endowed with the structure of a Hopf algebra.