Cohomology of the Lie algebra of Hamiltonian formal vector fields

1973 ◽  
Vol 6 (3) ◽  
pp. 193-196 ◽  
Author(s):  
I. M. Gel'fand ◽  
D. I. Kalinin ◽  
D. B. Fuks
Keyword(s):  
Lie Algebra ◽  
Vector Fields ◽  
Formal Vector

COHOMOLOGY OF THE LIE ALGEBRA OF FORMAL VECTOR FIELDS

1970 ◽  
Vol 4 (2) ◽  
pp. 327-342 ◽  
Author(s):  
I M Gel'fand ◽  
D B Fuks
Keyword(s):  
Lie Algebra ◽  
Vector Fields ◽  
Formal Vector

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].

scholarly journals Representations of the Lie algebra of vector fields on a sphere

2019 ◽  
Vol 223 (8) ◽  
pp. 3581-3593 ◽  
Author(s):  
Yuly Billig ◽  
Jonathan Nilsson
Keyword(s):  
Lie Algebra ◽  
Vector Fields
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