We discuss a method to construct a De Rham complex (differential algebra) of Poincar'e-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 colour Lie superalgebras.

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CWI
Department of Analysis, Algebra and Geometry [AM]

van den Hijligenberg, N.W, & Martini, R. (1995). Differential Hopf algebra structures on the universal enveloping algebra ofa Lie algebra. Department of Analysis, Algebra and Geometry [AM]. CWI.