A note on the algebra of Poisson brackets
1984 ◽
Vol 96
(1)
◽
pp. 45-60
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Keyword(s):
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].
2003 ◽
Vol 12
(05)
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pp. 589-604
Keyword(s):
1997 ◽
Vol 12
(22)
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pp. 1589-1595
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1992 ◽
Vol 47
(6)
◽
pp. 135-191
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2017 ◽
Vol 14
(11)
◽
pp. 1750160
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2001 ◽
Vol 03
(04)
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pp. 533-548
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Keyword(s):
Keyword(s):
2019 ◽
Vol 56
(3)
◽
pp. 280-296