Differential Hopf algebra structures on the universal enveloping algebra of a Lie algebra

N. van den Hijligenberg; R. Martini

Differential Hopf algebra structures on the universal enveloping algebra of a Lie algebra

N. van den Hijligenberg
, R. Martini

Discrete Mathematics and Mathematical Programming

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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
Place of Publication	Amsterdam
Publisher	Centrum voor Wiskunde en Informatica
Number of pages	8
Publication status	Published - 1995

Publication series

Name	CWI Report
Publisher	CWI
No.	AM-R9515
ISSN (Print)	0924-2953

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https://ir.cwi.nl/pub/4966

Differential Hopf algebra structures on the Universal Enveloping Algebra of a Lie Algebra
van den Hijligenberg, N. & Martini, R., 1995, In: Journal of mathematical physics. 37, p. 524-532 11 p.
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Differential Hopf algebra structures on the universal enveloping algebra of a Lie algebra

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Differential Hopf algebra structures on the Universal Enveloping Algebra of a Lie Algebra

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