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Apr
25
comment 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
comment 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
comment The Jacobi Identity for the Poisson Bracket
I find your answer to be the right complement to Jose's answer. Thanks.
Apr
23
revised 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
comment 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
comment 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 ?
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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.
Apr
16
comment On closed totally disconnected subgroups of connected real Lie groups
@Hugo Chapdelaine: does not your question concern Lie groups?