Logic behind one step of the proof of set of roots of a semisimple Lie algebra $\mathfrak{g}$ must span the dual vector space of its Cartan subalgebra

score 51 · Answer 7 · 2026-03-28 01:48:46

51

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Why is $(Ad\, x)^(u)(X) = u(Ad(x^{-1})X)$ for $u\in (T_eG)^$ and $X\in T_eG$?

Published on 28 Mar 2026 - 1:48

score 66 · Answer 8 · 2026-03-28 06:23:59

66

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Non-reductiveness of upper trianguler matrices $\mathfrak{t}_{n}$ as a Lie algebra

Published on 28 Mar 2026 - 6:23

score 139 · Answer 9 · 2026-04-11 09:19:16

139

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Pushforward and pullback on matrix Lie group

Published on 11 Apr 2026 - 9:19

score 81 · Answer 10 · 2023-06-03 07:32:09

81

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Prove that the adjoint representation is a smooth map

Published on 03 Jun 2023 - 7:32

score 65 · Answer 11 · 2026-03-25 03:01:35

65

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Length function on Weyl group $S_n$ gives part of the Pascal's triangle

Published on 25 Mar 2026 - 3:01

score 154 · Answer 12 · 2023-06-03 17:31:16

154

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Differential of conjugation map is smooth

Published on 03 Jun 2023 - 17:31

score 38 · Answer 13 · 2026-04-11 16:45:25

38

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How to calculate the trace of $ad(H)$ as a linear operator acting on $\mathfrak{g}_{n\alpha}$?

Published on 11 Apr 2026 - 16:45

score 74 · Answer 14 · 2026-04-12 15:48:51

74

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Precisely speaking, how can we understand Taylor series in the prespective of Lie Algebras?

Published on 12 Apr 2026 - 15:48

score 43 · Answer 15 · 2026-03-28 01:47:18

43

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Reference request, relation algebraic groups, real groups and their Lie algebras

Published on 28 Mar 2026 - 1:47

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Logic behind one step of the proof of set of roots of a semisimple Lie algebra $\mathfrak{g}$ must span the dual vector space of its Cartan subalgebra

Why is $(Ad\, x)^(u)(X) = u(Ad(x^{-1})X)$ for $u\in (T_eG)^$ and $X\in T_eG$?

Non-reductiveness of upper trianguler matrices $\mathfrak{t}_{n}$ as a Lie algebra

Pushforward and pullback on matrix Lie group

Prove that the adjoint representation is a smooth map

Length function on Weyl group $S_n$ gives part of the Pascal's triangle

Differential of conjugation map is smooth

How to calculate the trace of $ad(H)$ as a linear operator acting on $\mathfrak{g}_{n\alpha}$?

Precisely speaking, how can we understand Taylor series in the prespective of Lie Algebras?

Reference request, relation algebraic groups, real groups and their Lie algebras

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