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If $A(t)\in SO(3)$, why is $\dot{A}(t)A(t)^{-1}\in\mathfrak{so}(3)$?

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#lie-groups #lie-algebras
175
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matrix lie group

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#differential-geometry #lie-groups #lie-algebras
258
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How do I derive this formula from gauge theory?

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#differential-geometry #lie-groups #lie-algebras #differential-forms #gauge-theory
1.2k
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Free and proper action of a closed subgroup of a Lie group

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#lie-groups #smooth-manifolds #group-actions
57
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Inversion of Lie subspace in Cartan decomposition

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#lie-groups #lie-algebras #matrix-calculus #matrix-decomposition
55
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How to show that the metric $\frac{|dz|^2}{y^2}$ and the 2-form $\frac{dz \wedge d\overline{z}}{(-2i)y^2}$ are $SL_2$-invariant measures?

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#representation-theory #lie-groups #differential-forms #harmonic-analysis #hyperbolic-geometry
572
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Question about Bruhat decomposition for $SL_2$.

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#representation-theory #lie-groups
485
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Orbits of $SL(3, \mathbb{C})/B$

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#matrices #algebraic-geometry #lie-groups #algebraic-groups #homogeneous-spaces
1.4k
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Isoclinic rotations in four dimensions

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#differential-geometry #lie-groups #fiber-bundles #grassmannian
1.1k
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The Taylor series for product of Lie group elements

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#lie-groups #taylor-expansion #lie-algebras
195
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Action of discrete subgroup of Lie Groups

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#differential-geometry #differential-topology #lie-groups #topological-groups
359
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If a complex Lie group has the structure of an algebraic group, is this structure unique?

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#lie-groups #complex-geometry #algebraic-groups
186
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Does there exist an isotropic left invariant Riemannian metric on $GL_n^+$?

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#lie-groups #riemannian-geometry #curvature #symmetry
485
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Exponential of adjoint action notation confusion

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#notation #lie-groups
478
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Intersection of a family of closed Lie subgroups

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#lie-groups #lie-algebras

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