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Apr 27 |
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The Jacobi Identity for the Poisson Bracket
@Josè Figueroa-O'Farrill: Thanks for the attention. In my answer, I tried to highlight this point that was already in your answer. But my approach is lowbrow with respect to the highbrow answer of Jonathan. |
Apr 25 |
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Lie group operation and tangent vectors
About some of following answers: Excuse me, but is not the content of the question exactly to prove that $T_{e,e}\mu(\xi,\eta)=\xi+\eta$ for any $\xi,\eta\in T_eG$? So we should not appeal to it in a proof. But we should point out that this expression is just a consequence of the canonical identification of $T(G\times G)$ with the direct product $TG\times TG$. |
Apr 24 |
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The Jacobi Identity for the Poisson Bracket
@Josè Figueroa-O'Farrill: When, for an arbitrary almost-symplectic manifold, we again construct the bracket, is correct that $d\omega(X_f,X_g,X_h)$ is equal to the Jacobiator $J(f,g,h)$? or I am making same mistake? |
Apr 24 |
revised |
The Jacobi Identity for the Poisson Bracket
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Apr 23 |
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The Jacobi Identity for the Poisson Bracket
I find your answer to be the right complement to Jose's answer. Thanks. |
Apr 23 |
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regarding metric and symplectic forms
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Apr 23 |
answered | regarding metric and symplectic forms |
Apr 23 |
awarded | Nice Question |
Apr 23 |
revised |
The Jacobi Identity for the Poisson Bracket
I hope to have improved formatting |
Apr 23 |
answered | The Jacobi Identity for the Poisson Bracket |
Apr 21 |
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What is a Lagrangian submanifold intuitively?
@Stefan Waldmann: It is remarkable that first occurrences of Lagrangian submanifolds and even of the Fourier integral operators could be found in the pioneer work of Maslov. |
Apr 20 |
answered | Early Two-Author Math Papers |
Apr 19 |
awarded | Enlightened |
Apr 18 |
awarded | Nice Answer |
Apr 18 |
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On closed totally disconnected subgroups of connected real Lie groups
@Stephen: thanks a lot for your attention. |
Apr 17 |
revised |
How transitive are the actions of symplectomorphism groups ?
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Apr 17 |
revised |
How transitive are the actions of symplectomorphism groups ?
deleted 12 characters in body; edited body |
Apr 17 |
answered | How transitive are the actions of symplectomorphism groups ? |
Apr 16 |
answered | Deeper meanings of Phase Space — any books? |
Apr 16 |
comment |
What is an exponential?
@Hanno Becker @Steve Huntsman just a note: the group of invertible elements in a Banach algebra has natural structure of manifold modeled on the underlying Banach space, and I know Serge Lang's Foundamentals of Differential Geometry as the reference for Banach Manifolds. There the exponential map is associated to any spray on a Banach manifold. |