Realization of semisimple lie algebras with polynomial and rational vector fields

1993 ◽  
Vol 21 (11) ◽  
pp. 4065-4081 ◽  
Author(s):  
H. Gradl
Keyword(s):  
Lie Algebras ◽  
Vector Fields ◽  
Semisimple Lie Algebras ◽  
Rational Vector ◽  
Rational Vector Fields

scholarly journals Finitely Generated Algebras Associated with Rational Vector Fields

1997 ◽  
Vol 198 (2) ◽  
pp. 481-498
Author(s):  
Hisayo Aoki ◽  
Masayoshi Miyanishi
Keyword(s):  
Vector Fields ◽  
Finitely Generated ◽  
Rational Vector ◽  
Rational Vector Fields

A note on the algebra of Poisson brackets

1984 ◽  
Vol 96 (1) ◽  
pp. 45-60 ◽  
Author(s):  
C. J. Atkin
Keyword(s):  
Poisson Bracket ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Symplectic Manifold ◽  
Vector Fields ◽  
Poisson Brackets ◽  
Infinite Dimensional

In a long sequence of notes in the Comptes Rendus and elsewhere, and in the papers [1], [2], [3], [6], [7], Lichnerowicz and his collaborators have studied the ‘classical infinite-dimensional Lie algebras’, their derivations, automorphisms, co-homology, and other properties. The most familiar of these algebras is the Lie algebra of C∞ vector fields on a C∞ manifold. Another is the Lie algebra of ‘Poisson brackets’, that is, of C∞ functions on a C∞ symplectic manifold, with the Poisson bracket as composition; some questions concerning this algebra are of considerable interest in the theory of quantization – see, for instance, [2] and [3].

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