THE ALGEBRA OF DIFFERENTIAL FORMS ON A FULL MATRIC BIALGEBRA

We construct a non-commutative analogue of the algebra of differential forms on the space of endomorphisms of a vector space, given a non-co mmutative algebra of functions and differential forms on the vector sp ace. The construction yields a differential bialgebra which is a skew product of an algebra of functions and an algebra of differential form s with constant coefficients. We give necessary and sufficient conditi ons for such an algebra to exist, show that it is uniquely determined by the differential algebra on the vector space, and show that it is a non-commutative superpolynomial algebra in the matrix elements and th eir differentials (i.e. that it has the same dimensions of homogeneous components as in the classical case).