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Differential Hopf algebra structures on the universal enveloping algebra ofa Lie algebra

By N.W. van den Hijligenberg and R. Martini


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

Publisher: CWI
Year: 1995
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