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Lie transformation applied to Poisson brackets

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#linear-algebra #lie-groups #lie-algebras
259
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Is the exponential map of complex spin group surjective?

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#lie-groups #lie-algebras
804
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Killing fields and symmetries

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#differential-geometry #symmetry #lie-algebras #vector-fields
75
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Can the parameter $t$ in the exponential map $e^{tX}$ be complex?

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#lie-groups #lie-algebras
2k
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Lie algebra of the automorphism group of a Lie group?

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#lie-groups #lie-algebras
197
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Lie functor produces an antihomomorphism in Lavendhomme's synthetic differential geometry text?

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#differential-geometry #lie-groups #lie-algebras #synthetic-differential-geometry
2.8k
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$su(2) $ and $ sl(2;R)$ are not isomorphic?

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#lie-groups #lie-algebras
548
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Adjoint action on Lie algebra su(2) ($A \in SU(2), X \in \mathfrak{su(2)} \Rightarrow AXA^{-1}\in \mathfrak{su(2)}$)

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#lie-groups #lie-algebras #matrix-calculus #adjoint-operators
102
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The simplest way to present a Lie algebra to a wide audience?

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#terminology #lie-groups #lie-algebras
384
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One-parameter subgroups and Lie bracket

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#differential-geometry #lie-groups #lie-algebras
42
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Normal subgroup of Engel group

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#proof-verification #lie-groups #lie-algebras #topological-groups #normal-subgroups
599
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The condition for the exponential map of Lie group is surjective or injective

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#lie-groups #lie-algebras
84
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Relating ${\rm ad}(\phi(X))$ with $\phi \circ\,{\rm ad}(X) \circ \phi^{-1}$.

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#abstract-algebra #lie-algebras #adjoint-operators
70
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Treatments of Lie theory and Noether theorems in tensor notation

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#reference-request #lie-groups #lie-algebras #book-recommendation #tensors
99
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Why do we need finite dimension for this diagram to commute?

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#abstract-algebra #lie-algebras

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