Class: 'Poisson structure'
http://cll.niimm.ksu.ru/ontologies/mathematics#E3234
Annotations (3)
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comment "A Poisson structure on $M$ is a bilinear map
$$\{.,.\}:C^\infty(M)xC^\infty(M) \to C^\infty(M)$$
with the following properties:
1. It is skew symmetric: $\{f,g\} = −\{g,f\}$.
2. It obeys the Jacobi identity:$ \{f,\{g,h\}\} + \{g,\{h,f\}\} +\ {h,\{f,g\}\} = 0$.
3. It is a derivation of $C^\infty(M)$ in its first argument: $\{fg,h\} = f{g,h} + g\{f,h\}$.
" (en)
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label "Poisson structure" (en)
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label "Пуассонова структура" (ru)
Equivalents (2)
Superclasses (1)
Usage (1)
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Class: 'Poisson structure'