In mathematics, a Poisson algebra is an associative algebra together with a Lie bracket that also satisfies Leibniz's law; that is, the bracket is also...
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more general sense, the Poisson bracket is used to define a Poisson algebra, of which the algebra of functions on a Poisson manifold is a special case...
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In mathematics, a Poisson superalgebra is a Z2-graded generalization of a Poisson algebra. Specifically, a Poisson superalgebra is an (associative) superalgebra...
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{\displaystyle M} , making it into a Lie algebra subject to a Leibniz rule (also known as a Poisson algebra). Poisson structures on manifolds were introduced...
61 KB (9,227 words) - 13:51, 23 July 2024
Hamiltonian mechanics (section Poisson algebras)
Poisson bracket without resorting to differential equations, see Lie algebra; a Poisson bracket is the name for the Lie bracket in a Poisson algebra....
52 KB (9,273 words) - 03:43, 13 September 2024
mathematics, a Poisson–Lie group is a Poisson manifold that is also a Lie group, with the group multiplication being compatible with the Poisson algebra structure...
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Baron Siméon Denis Poisson FRS FRSE (French: [si.me.ɔ̃ də.ni pwa.sɔ̃]; 21 June 1781 – 25 April 1840) was a French mathematician and physicist who worked...
34 KB (4,390 words) - 03:17, 18 September 2024
deformation quantization of the corresponding Poisson algebra. It is due to Maxim Kontsevich. Given a Poisson algebra (A, {⋅, ⋅}), a deformation quantization...
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In differential geometry a Poisson supermanifold is a differential supermanifold M such that the supercommutative algebra of smooth functions over it (to...
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theory as the algebra of generalized Poisson brackets defined on differential forms. A Gerstenhaber algebra is a graded-commutative algebra with a Lie bracket...
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