List questions from lie-groups

Published on 16 Dec 2014 - 2:58

2.3k

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Are there common inequivalent definitions of Cartan subalgebra of a real Lie algebra?

Published on 17 Dec 2014 - 0:31

1.6k

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Directional derivative of the determinant

Published on 18 Dec 2014 - 12:39

529

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What's wrong with this trivial proof that every element of a compact Lie group is contained in a maximal torus?

Published on 19 Dec 2014 - 2:48

46

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$B$-action on $U$.

Published on 26 Mar 2026 - 17:51

80

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Proving a relation for representations of gauge groups

Published on 19 Dec 2014 - 17:24

792

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Relation between simple roots and fundamental weights.

Published on 26 Mar 2026 - 1:27

127

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Dimension of image of Lie bracket

Published on 23 Dec 2014 - 11:58

1.5k

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Help needed in understanding the basics of Cartan decomposition of a Lie algebra

Published on 23 Dec 2014 - 21:42

81

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Shouldn't this be "injective" rather than "well-defined"?

Published on 24 Dec 2014 - 23:48

100

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Group of isometries is closed in $GL_{n+1}$

Published on 29 Mar 2026 - 6:33

2.3k

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Need help with proof of $SO(3)$ is path connected

Published on 26 Dec 2014 - 6:29

263

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Algebra of matrix coefficient over a compact group is isomorphic to its dual.

Published on 26 Dec 2014 - 12:52

387

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Help understanding the argument used in this proof that $SO(n)$ is path-connected

Published on 27 Dec 2014 - 1:21

2.3k

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Why are root spaces of root decomposition of semisimple Lie algebra 1 dimensional?

Published on 25 Mar 2026 - 22:06

List Question

These subsets of $O(n)$ are clopen

Are there common inequivalent definitions of Cartan subalgebra of a real Lie algebra?

Directional derivative of the determinant

What's wrong with this trivial proof that every element of a compact Lie group is contained in a maximal torus?

$B$-action on $U$.

Proving a relation for representations of gauge groups

Relation between simple roots and fundamental weights.

Dimension of image of Lie bracket

Help needed in understanding the basics of Cartan decomposition of a Lie algebra

Shouldn't this be "injective" rather than "well-defined"?

Group of isometries is closed in $GL_{n+1}$

Need help with proof of $SO(3)$ is path connected

Algebra of matrix coefficient over a compact group is isomorphic to its dual.

Help understanding the argument used in this proof that $SO(n)$ is path-connected

Why are root spaces of root decomposition of semisimple Lie algebra 1 dimensional?

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