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Conjugation by the transpose homomorphism

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#abstract-algebra #group-theory #lie-groups #group-homomorphism
665
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Invariant metric of a matrix Lie Group as induced metric in R^(n^2)

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#differential-geometry #lie-groups
96
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Integral orthogonal group generated by unipotent elements?

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#group-theory #number-theory #lie-groups #quadratic-forms
592
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how to define multivariete normal distribution on sphere

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#probability-distributions #lie-groups #normal-distribution #lie-algebras
59
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action of an ismorphic tangent space

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#differential-geometry #definition #lie-groups #lie-algebras
495
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Root decomposition implies semisimple

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#lie-groups #lie-algebras #root-systems
39
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Convergence to uniform of a finite subsets of free subgroup in $SO(3)$.

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#probability #lie-groups #ergodic-theory #haar-measure
175
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If the derivative map at the identity is bijective, then all derivitive maps are bijective

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#manifolds #lie-groups #lie-algebras #tangent-bundle
75
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$\mathfrak{g}$-module structure on the tensor algebra $T(g)$

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#abstract-algebra #lie-groups #lie-algebras
35
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Embedding corresponding to a representation

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#representation-theory #lie-groups #lie-algebras
171
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Is $sl(n,C)$ itself an irreducible representation of $SL(n,C)$

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#representation-theory #lie-groups #lie-algebras
72
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How is the coadjoint action of $\mathfrak {g}^{\ast}$ on $\mathfrak {g}$ defined?

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#lie-groups #lie-algebras #coadjoint-action #adjoint-action
139
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Question about structures of $SO(3)$ and the elements in $SO(3)$

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#lie-groups #lie-algebras #smooth-manifolds
348
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Jordan form of an orthogonal matrix

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#linear-algebra #matrices #lie-groups #jordan-normal-form #linear-groups
81
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How do we prove that $H$ is a Lie group?

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#lie-groups #lie-algebras

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