Question

Prove that 1. $\kappa(x,y)$ is a symmetric bilinear form? 2. $\kappa([x,y],z)=\kappa(x,[y,z])$

score 128 · Answer 1 · 2026-03-22 16:38:17

128

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Prove that 1. $\kappa(x,y)$ is a symmetric bilinear form? 2. $\kappa([x,y],z)=\kappa(x,[y,z])$

Published on 22 Mar 2026 - 16:38

score 666 · Answer 2 · 2026-03-17 04:57:30

666

Views

Show that $ad(X)$ is also diagonalisable.

Published on 17 Mar 2026 - 4:57

score 478 · Answer 3 · 2026-03-22 23:24:46

478

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How does the non-degenerate symmetric bilinear form on $\mathfrak{h}$ induce a non-degenerate symmetric bilinear form on $\mathfrak{h}^*$?

Published on 22 Mar 2026 - 23:24

score 55 · Answer 4 · 2026-03-22 13:53:17

55

Views

Iwasawa decomposition for real Grassmannians

Published on 22 Mar 2026 - 13:53

score 999 · Answer 5 · 2018-02-22 06:20:48

999

Views

Adjoint representation of $\mathfrak{so}(n)$

Published on 22 Feb 2018 - 6:20

score 74 · Answer 6 · 2026-03-22 23:15:34

74

Views

Adjoint orbit of an regular and elliptic element of $\mathrm{SP}(2n,\mathbb{R})$

Published on 22 Mar 2026 - 23:15

score 36 · Answer 7 · 2026-03-20 12:56:51

36

Views

How to get an isomorphic ideal from a given one?

Published on 20 Mar 2026 - 12:56

score 674 · Answer 8 · 2026-03-17 14:23:33

674

Views

What is the mistake in finding the irreps of $SU(3)$ multiplets $6 \otimes 8$, or $15 \otimes \bar{15}$?

Published on 17 Mar 2026 - 14:23

score 49 · Answer 9 · 2026-03-25 07:43:56

49

Views

Fulton-Harris: Action by negative roots generates and irreducible representation

Published on 25 Mar 2026 - 7:43

score 238 · Answer 10 · 2026-03-22 21:49:05

238

Views

A question on the proof of Gelfand-Kazhdan theorem.

Published on 22 Mar 2026 - 21:49

score 268 · Answer 11 · 2026-03-22 22:46:33

268

Views

The exponential function and one-parameter subgroups

Published on 22 Mar 2026 - 22:46

score 277 · Answer 12 · 2018-02-23 23:00:46

277

Views

How does the universal enveloping algebra of a Lie algebra act on its Lie group?

Published on 23 Feb 2018 - 23:00

score 312 · Answer 13 · 2018-02-24 11:30:46

312

Views

Proof of conjugacy of Cartan subalgebras

Published on 24 Feb 2018 - 11:30

score 65 · Answer 14 · 2026-03-23 11:01:34

65

Views

Question on nomenclature of ... mappings?

Published on 23 Mar 2026 - 11:01

score 136 · Answer 15 · 2026-03-25 09:26:35

136

Views

Two questions about the Killing Form in Fulton-Harris

Published on 25 Mar 2026 - 9:26

List Question

Prove that 1. $\kappa(x,y)$ is a symmetric bilinear form? 2. $\kappa([x,y],z)=\kappa(x,[y,z])$

Show that $ad(X)$ is also diagonalisable.

How does the non-degenerate symmetric bilinear form on $\mathfrak{h}$ induce a non-degenerate symmetric bilinear form on $\mathfrak{h}^*$?

Iwasawa decomposition for real Grassmannians

Adjoint representation of $\mathfrak{so}(n)$

Adjoint orbit of an regular and elliptic element of $\mathrm{SP}(2n,\mathbb{R})$

How to get an isomorphic ideal from a given one?

What is the mistake in finding the irreps of $SU(3)$ multiplets $6 \otimes 8$, or $15 \otimes \bar{15}$?

Fulton-Harris: Action by negative roots generates and irreducible representation

A question on the proof of Gelfand-Kazhdan theorem.

The exponential function and one-parameter subgroups

How does the universal enveloping algebra of a Lie algebra act on its Lie group?

Proof of conjugacy of Cartan subalgebras

Question on nomenclature of ... mappings?

Two questions about the Killing Form in Fulton-Harris

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