Question

What are the eigenvalues and eigenvectors of $\operatorname{ad}x$ for non-diagonalizable $x$?

score 119 · Answer 1 · 2026-03-20 13:55:29

119

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What are the eigenvalues and eigenvectors of $\operatorname{ad}x$ for non-diagonalizable $x$?

Published on 20 Mar 2026 - 13:55

score 50 · Answer 2 · 2026-04-17 18:57:24

50

Views

What is the exact definition of the "index" which matches the determinant of the Cartan matrix and how to prove the equivalence?

Published on 17 Apr 2026 - 18:57

score 21 · Answer 3 · 2026-03-25 20:36:39

21

Views

The action of Minimal Kac-Moody group on its Lie algebra

Published on 25 Mar 2026 - 20:36

score 36 · Answer 4 · 2026-03-28 11:33:34

36

Views

How to derive explicit matrix representations for the non-diagonal generators of a simple Lie algebra?

Published on 28 Mar 2026 - 11:33

score 25 · Answer 5 · 2026-04-13 20:02:00

The associated Lie algebra of the unital associative algebra $\mathcal{A}$ in the Universal Enveloping Algebras

score 69 · Answer 6 · 2026-04-16 13:24:02

69

Views

What is in the image of the exponential of $\frak{sl}(n,\mathbb{R}$)? What do you need to get all of $\mathrm{SL}(n,\mathbb{R}$)?

Published on 16 Apr 2026 - 13:24

score 50 · Answer 7 · 2026-03-26 06:34:58

50

Views

how to prove the Lemma 5.6. of "Invitation to 3D vision"

Published on 26 Mar 2026 - 6:34

score 41 · Answer 8 · 2026-04-13 22:41:17

41

Views

Constructing the finite-dimensional representations of $\frak{sl}_3$

Published on 13 Apr 2026 - 22:41

score 130 · Answer 9 · 2026-04-13 21:23:27

130

Views

Are "infinitesimal rotations" commutative? If so, which mathematical fact allows it?

Published on 13 Apr 2026 - 21:23

score 41 · Answer 10 · 2026-04-12 10:51:35

41

Views

Is this representation of a Lie algebra decomposable?

Published on 12 Apr 2026 - 10:51

score 64 · Answer 11 · 2026-03-25 04:44:19

If we have two Dynkin diagrams such that $D_{1}$ is a subdiagram of $D_{2}$. Then the $\mathfrak{g}(R_{1})$ is a subalgebra of $\mathfrak{g}(R_{2})$

score 4.9k · Answer 12 · 2026-04-15 10:52:34

4.9k

Views

Exponential map is surjective for compact connected Lie group

Published on 15 Apr 2026 - 10:52

score 201 · Answer 13 · 2026-04-14 08:58:51

201

Views

Irreducible Representations of Nilpotent Lie algebras

Published on 14 Apr 2026 - 8:58

score 62 · Answer 14 · 2026-04-10 07:01:20

62

Views

Notation in Kac Problem 3.2

Published on 10 Apr 2026 - 7:01

score 551 · Answer 15 · 2026-04-14 05:12:13

551

Views

Tensor product over Lie group isomorphic to that over its Lie algebra

Published on 14 Apr 2026 - 5:12

List Question

What are the eigenvalues and eigenvectors of $\operatorname{ad}x$ for non-diagonalizable $x$?

What is the exact definition of the "index" which matches the determinant of the Cartan matrix and how to prove the equivalence?

The action of Minimal Kac-Moody group on its Lie algebra

How to derive explicit matrix representations for the non-diagonal generators of a simple Lie algebra?

The associated Lie algebra of the unital associative algebra $\mathcal{A}$ in the Universal Enveloping Algebras

What is in the image of the exponential of $\frak{sl}(n,\mathbb{R}$)? What do you need to get all of $\mathrm{SL}(n,\mathbb{R}$)?

how to prove the Lemma 5.6. of "Invitation to 3D vision"

Constructing the finite-dimensional representations of $\frak{sl}_3$

Are "infinitesimal rotations" commutative? If so, which mathematical fact allows it?

Is this representation of a Lie algebra decomposable?

If we have two Dynkin diagrams such that $D_{1}$ is a subdiagram of $D_{2}$. Then the $\mathfrak{g}(R_{1})$ is a subalgebra of $\mathfrak{g}(R_{2})$

Exponential map is surjective for compact connected Lie group

Irreducible Representations of Nilpotent Lie algebras

Notation in Kac Problem 3.2

Tensor product over Lie group isomorphic to that over its Lie algebra

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