### Abstract

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.

Original language | English |
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Place of Publication | Amsterdam |

Publisher | C.W.I. |

Number of pages | 8 |

Publication status | Published - 1995 |

### Publication series

Name | Report / Department of Algebra, Analysis and Geometry |
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Publisher | CWI |

No. | AM-R9515 |

### Keywords

- METIS-141351
- IR-102315

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## Cite this

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.