DIFFERENTIAL HOPF ALGEBRA STRUCTURES ON THE UNIVERSAL ENVELOPING ALGEBRA OF A LIE ALGEBRA

摘要

We discuss a method to construct a De Rham complex (differential algebra) of Poincare-Birkhoff-Witt type on the universal enveloping algebra of a Lie algebra g. We determine the cases in which this gives rise to a differential Hopf algebra that naturally extends the Hopf algebra structure of U(g) The construction of such differential structures is interpreted in terms of color Lie superalgebras. (C) 1996 American Institute of Physics. [References: 13]