Structures on manifolds | Smooth manifolds | Symplectic geometry | Differential geometry

Poisson manifold

In differential geometry, a Poisson structure on a smooth manifold is a Lie bracket (called a Poisson bracket in this special case) on the algebra of smooth functions on , subject to the Leibniz rule . Equivalently, defines a Lie algebra structure on the vector space of smooth functions on such that is a vector field for each smooth function (making into a Poisson algebra). Poisson structures on manifolds were introduced by André Lichnerowicz in 1977. They were further studied in the classical paper of Alan Weinstein, where many basic structure theorems were first proved, and which exerted a huge influence on the development of Poisson geometry — which today is deeply entangled with non-commutative geometry, integrable systems, topological field theories and representation theory, to name a few. Poisson structures are named after the French mathematician Siméon Denis Poisson, due to their early appearance in his works on analytical mechanics. (Wikipedia).

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Brent Pym: Holomorphic Poisson structures - lecture 2

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From playlist Virtual Conference

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From playlist Virtual Conference

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From playlist Course 8: Fourier Analysis

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From playlist Physics

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From playlist HIM Lectures: Trimester Program "Symplectic Geometry and Representation Theory"

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From playlist Manifolds

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From playlist Manifolds

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From playlist Global Noncommutative Geometry Seminar (Americas)

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From playlist Topology

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From playlist Virtual Conference

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Math 139 Fourier Analysis Lecture 20: Steady-state heat equation in the upper half plane

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From playlist Course 8: Fourier Analysis

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From playlist Mathematics

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From playlist Landau-Ginzburg seminar

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From playlist VIRTUAL EVENT GEOMETRIC GROUP THEORY CONFERENCE

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From playlist Geometry

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From playlist MATRIX-SMRI Symposium: Nijenhuis Geometry companion lectures (Sino-Russian Mathematical Centre)

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From playlist Classical Physics by Parth G

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