Differential Calculi of Poincare-Birkhoff-Witt type on Universal Enveloping Algebras

R. Martini; G.F. Post; P.H.M. Kersten

doi:10.48550/arXiv.q-alg/9506010

Differential Calculi of Poincare-Birkhoff-Witt type on Universal Enveloping Algebras

R. Martini
, G.F. Post
, P.H.M. Kersten

Discrete Mathematics and Mathematical Programming

Research output: Working paper › Preprint › Academic

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Abstract

Differential calculi of Poincare-Birkhoff-Witt type on universal enveloping algebras of Lie algebras g are defined. This definition turns out to be independent of the basis chosen in g. The role of automorphisms of g is explained. It is proved that no differential calculus of Poincare-Birkhoff-Witt type exists on semi-simple Lie algebras. Examples are given, namely gl_n, Abelian Lie algebras, the Heisenberg algebra, the Witt and the Virasoro algebra. Completely treated are the 2-dimensional solvable Lie algebra, and the 3-dimensional Heisenberg algebra.

Original language	English
Publisher	ArXiv.org
DOIs	https://doi.org/10.48550/arXiv.q-alg/9506010
Publication status	Published - 9 Jun 1995

Keywords

q-alg
math.QA

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10.48550/arXiv.q-alg/9506010

9506010v3Final published version, 117 KB

Quantization of differential calculi on universal enveloping algebras
van den Hijligenberg, N., Martini, R. & Post, G. F., 1996, In: Journal of mathematical physics. 37, p. 4166-4175 10 p.
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abstract = "Differential calculi of Poincare-Birkhoff-Witt type on universal enveloping algebras of Lie algebras g are defined. This definition turns out to be independent of the basis chosen in g. The role of automorphisms of g is explained. It is proved that no differential calculus of Poincare-Birkhoff-Witt type exists on semi-simple Lie algebras. Examples are given, namely gl\_n, Abelian Lie algebras, the Heisenberg algebra, the Witt and the Virasoro algebra. Completely treated are the 2-dimensional solvable Lie algebra, and the 3-dimensional Heisenberg algebra. ",

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Y1 - 1995/6/9

N2 - Differential calculi of Poincare-Birkhoff-Witt type on universal enveloping algebras of Lie algebras g are defined. This definition turns out to be independent of the basis chosen in g. The role of automorphisms of g is explained. It is proved that no differential calculus of Poincare-Birkhoff-Witt type exists on semi-simple Lie algebras. Examples are given, namely gl_n, Abelian Lie algebras, the Heisenberg algebra, the Witt and the Virasoro algebra. Completely treated are the 2-dimensional solvable Lie algebra, and the 3-dimensional Heisenberg algebra.

AB - Differential calculi of Poincare-Birkhoff-Witt type on universal enveloping algebras of Lie algebras g are defined. This definition turns out to be independent of the basis chosen in g. The role of automorphisms of g is explained. It is proved that no differential calculus of Poincare-Birkhoff-Witt type exists on semi-simple Lie algebras. Examples are given, namely gl_n, Abelian Lie algebras, the Heisenberg algebra, the Witt and the Virasoro algebra. Completely treated are the 2-dimensional solvable Lie algebra, and the 3-dimensional Heisenberg algebra.

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BT - Differential Calculi of Poincare-Birkhoff-Witt type on Universal Enveloping Algebras

PB - ArXiv.org

ER -

Differential Calculi of Poincare-Birkhoff-Witt type on Universal Enveloping Algebras

Abstract

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Research output

Quantization of differential calculi on universal enveloping algebras

Cite this