Question

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

score 137 · Answer 1 · 2026-05-10 16:55:05

137

Views

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

Published on 10 May 2026 - 16:55

score 671 · Answer 2 · 2026-05-10 13:49:12

671

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

Published on 10 May 2026 - 13:49

score 485 · Answer 3 · 2026-04-29 12:25:56

485

Views

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

Published on 29 Apr 2026 - 12:25

score 64 · Answer 4 · 2026-05-10 16:29:35

64

Views

Iwasawa decomposition for real Grassmannians

Published on 10 May 2026 - 16:29

score 1k · Answer 5 · 2026-04-17 09:32:05

1k

Views

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

Published on 17 Apr 2026 - 9:32

score 80 · Answer 6 · 2026-04-29 12:50:07

80

Views

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

Published on 29 Apr 2026 - 12:50

score 41 · Answer 7 · 2026-04-29 12:21:50

41

Views

How to get an isomorphic ideal from a given one?

Published on 29 Apr 2026 - 12:21

score 681 · Answer 8 · 2026-05-04 02:10:07

681

Views

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

Published on 04 May 2026 - 2:10

score 51 · Answer 9 · 2026-04-13 02:35:46

51

Views

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

Published on 13 Apr 2026 - 2:35

score 243 · Answer 10 · 2026-04-29 12:51:36

243

Views

A question on the proof of Gelfand-Kazhdan theorem.

Published on 29 Apr 2026 - 12:51

score 274 · Answer 11 · 2026-04-29 12:52:45

274

Views

The exponential function and one-parameter subgroups

Published on 29 Apr 2026 - 12:52

score 281 · Answer 12 · 2026-05-10 16:35:00

281

Views

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

Published on 10 May 2026 - 16:35

score 315 · Answer 13 · 2026-04-10 21:04:22

315

Views

Proof of conjugacy of Cartan subalgebras

Published on 10 Apr 2026 - 21:04

score 72 · Answer 14 · 2026-04-29 12:48:39

72

Views

Question on nomenclature of ... mappings?

Published on 29 Apr 2026 - 12:48

score 138 · Answer 15 · 2026-04-09 14:42:27

138

Views

Two questions about the Killing Form in Fulton-Harris

Published on 09 Apr 2026 - 14:42

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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