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

N. van den Hijligenberg; R. Martini

doi:10.1063/1.531407

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

N. van den Hijligenberg
, R. Martini

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Abstract

We discuss a method to construct a De Rham complex (differential algebra) of Poincaré–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 algebrastructure of U(g). The construction of such differential structures is interpreted in terms of color Lie superalgebras.

Original language	English
Pages (from-to)	524-532
Number of pages	11
Journal	Journal of mathematical physics
Volume	37
DOIs	https://doi.org/10.1063/1.531407
Publication status	Published - 1995

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10.1063/1.531407

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Differential Hopf algebra structures on the universal enveloping algebra of a Lie algebra
van den Hijligenberg, N. & Martini, R., 1995, Amsterdam: Centrum voor Wiskunde en Informatica. 8 p. (CWI Report; no. AM-R9515)
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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 algebrastructure of U(g). The construction of such differential structures is interpreted in terms of color Lie superalgebras.",

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AB - We discuss a method to construct a De Rham complex (differential algebra) of Poincaré–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 algebrastructure of U(g). The construction of such differential structures is interpreted in terms of color Lie superalgebras.

U2 - 10.1063/1.531407

DO - 10.1063/1.531407

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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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