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.
|Place of Publication||Amsterdam|
|Number of pages||8|
|Publication status||Published - 1995|
|Name||Report / Department of Algebra, Analysis and Geometry|
van den Hijligenberg, N. W., van den Hijligenberg, N. W., & Martini, R. (1995). Differential Hopf algebra structures on the universal enveloping algebra of a Lie algebra. (Report / Department of Algebra, Analysis and Geometry; No. AM-R9515). Amsterdam: C.W.I.