List questions from lie-groups

Published on 28 Mar 2026 - 2:23

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How to tell the rank of a semisimple Lie algebra?

Published on 25 Mar 2026 - 2:24

67

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Proving operator equality with exponentials

Published on 26 Mar 2026 - 3:09

696

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Proof of Lie's theorem, how to obtain a Lie group homomorphism from a Lie algebra homomorphism

Published on 28 Mar 2026 - 2:24

79

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Dual Total Differential operator

Published on 31 Oct 2018 - 20:40

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Why is $SU(2)$ diffeomorphic to $S^3$?

Published on 02 Nov 2018 - 4:26

818

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Universal cover of $SL_2(\mathbb{R})$ and Metaplectic group

Published on 25 Mar 2026 - 17:40

59

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Let $V$ be a complex representation of a compact Lie group $G$. Prove that $\overline{V}$ and $V^*$ are isomorphic representations of $G$.

Published on 04 Nov 2018 - 8:09

1.1k

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The map from SU(4) to SO(6)

Published on 05 Nov 2018 - 3:47

58

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The space of oriented 2-dimensional subspaces of $\mathbb{R}^4$ is compact and connected.

Published on 25 Mar 2026 - 23:37

68

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Connectedness of $GL_n(\mathbf{R}^{+})

Published on 26 Mar 2026 - 2:45

313

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Why are Klein geometries $G/H$?

Published on 27 Mar 2026 - 0:40

369

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Tangent Space and Charts

Published on 25 Mar 2026 - 4:36

77

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Confusion about the expansion of $\mathfrak{u}(n)$ in some arbitrary basis

Published on 11 Nov 2018 - 18:53

120

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Conjugacy classes of the Lie group $Sp(6,\mathbb{R})$

Published on 12 Nov 2018 - 16:39

List Question

If $[X, Y]=0$, then $\operatorname{Ad}_{e^{tX}}Y = Y$ for all $t\in \mathbb{R}$?

How to tell the rank of a semisimple Lie algebra?

Proving operator equality with exponentials

Proof of Lie's theorem, how to obtain a Lie group homomorphism from a Lie algebra homomorphism

Dual Total Differential operator

Why is $SU(2)$ diffeomorphic to $S^3$?

Universal cover of $SL_2(\mathbb{R})$ and Metaplectic group

Let $V$ be a complex representation of a compact Lie group $G$. Prove that $\overline{V}$ and $V^*$ are isomorphic representations of $G$.

The map from SU(4) to SO(6)

The space of oriented 2-dimensional subspaces of $\mathbb{R}^4$ is compact and connected.

Connectedness of $GL_n(\mathbf{R}^{+})

Why are Klein geometries $G/H$?

Tangent Space and Charts

Confusion about the expansion of $\mathfrak{u}(n)$ in some arbitrary basis

Conjugacy classes of the Lie group $Sp(6,\mathbb{R})$

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