A natural differential calculus on Lie bialgebras with dual of triangular type

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

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Abstract

We prove that for a specific class of Lie bialgebras, there exists a natural differential calculus. This class consists of the Lie bialgebras for which the dual Lie bialgebra is of triangular type. The differential calculus is explicitly constructed with the help of the $R$-matrix from the dual. The method is illustrated by several examples.
Original languageEnglish
Place of PublicationAmsterdam
PublisherStichting Mathematisch Centrum
Number of pages7
Publication statusPublished - 1995

Publication series

NameReport / Department of Algebra, Analysis and Geometry
PublisherStichting Mathematisch Centrum
No.Report AM-R9519

Fingerprint

Lie Bialgebra
Differential Calculus
Triangular
R-matrix
Class

Keywords

  • METIS-141350
  • IR-102316

Cite this

van den Hijligenberg, N., van den Hijligenberg, N. W., & Martini, R. (1995). A natural differential calculus on Lie bialgebras with dual of triangular type. (Report / Department of Algebra, Analysis and Geometry; No. Report AM-R9519). Amsterdam: Stichting Mathematisch Centrum.
van den Hijligenberg, N. ; van den Hijligenberg, N.W. ; Martini, Ruud. / A natural differential calculus on Lie bialgebras with dual of triangular type. Amsterdam : Stichting Mathematisch Centrum, 1995. 7 p. (Report / Department of Algebra, Analysis and Geometry; Report AM-R9519).
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van den Hijligenberg, N, van den Hijligenberg, NW & Martini, R 1995, A natural differential calculus on Lie bialgebras with dual of triangular type. Report / Department of Algebra, Analysis and Geometry, no. Report AM-R9519, Stichting Mathematisch Centrum, Amsterdam.

A natural differential calculus on Lie bialgebras with dual of triangular type. / van den Hijligenberg, N.; van den Hijligenberg, N.W.; Martini, Ruud.

Amsterdam : Stichting Mathematisch Centrum, 1995. 7 p. (Report / Department of Algebra, Analysis and Geometry; No. Report AM-R9519).

Research output: Book/ReportReportProfessional

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van den Hijligenberg N, van den Hijligenberg NW, Martini R. A natural differential calculus on Lie bialgebras with dual of triangular type. Amsterdam: Stichting Mathematisch Centrum, 1995. 7 p. (Report / Department of Algebra, Analysis and Geometry; Report AM-R9519).