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

N.W. van den Hijligenberg; N. van den Hijligenberg; Ruud Martini

doi:10.1063/1.531407

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

N.W. van den Hijligenberg, N. van den Hijligenberg, Ruud 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	Undefined
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

Keywords

IR-102317
METIS-140397

Access to Document

10.1063/1.531407

Hijligenberg95differential

http://dx.doi.org/10.1063/1.530124

Cite this

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title = "Differential Hopf algebra structures on the Universal Enveloping Algebra of a Lie Algebra",

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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AU - van den Hijligenberg, N.

AU - Martini, Ruud

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Y1 - 1995

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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.

KW - IR-102317

KW - METIS-140397

U2 - 10.1063/1.531407

DO - 10.1063/1.531407

M3 - Article

SN - 0022-2488

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EP - 532

JO - Journal of mathematical physics

JF - Journal of mathematical physics

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