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

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

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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 languageEnglish
Place of PublicationAmsterdam
PublisherC.W.I.
Number of pages8
Publication statusPublished - 1995

Publication series

NameReport / Department of Algebra, Analysis and Geometry
PublisherCWI
No.AM-R9515

Fingerprint

Differential Algebra
Universal Enveloping Algebra
Hopf Algebra
Lie Algebra
Lie Superalgebra
Color

Keywords

  • METIS-141351
  • IR-102315

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.
van den Hijligenberg, N.W. ; van den Hijligenberg, N.W. ; Martini, Ruud. / Differential Hopf algebra structures on the universal enveloping algebra of a Lie algebra. Amsterdam : C.W.I., 1995. 8 p. (Report / Department of Algebra, Analysis and Geometry; AM-R9515).
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van den Hijligenberg, NW, van den Hijligenberg, NW & 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, C.W.I., Amsterdam.

Differential Hopf algebra structures on the universal enveloping algebra of a Lie algebra. / van den Hijligenberg, N.W.; van den Hijligenberg, N.W.; Martini, Ruud.

Amsterdam : C.W.I., 1995. 8 p. (Report / Department of Algebra, Analysis and Geometry; No. AM-R9515).

Research output: Book/ReportReportProfessional

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van den Hijligenberg NW, van den Hijligenberg NW, Martini R. Differential Hopf algebra structures on the universal enveloping algebra of a Lie algebra. Amsterdam: C.W.I., 1995. 8 p. (Report / Department of Algebra, Analysis and Geometry; AM-R9515).