Question

Casimir element of a representation of a semi-simple Lie algebra

score 195 · Answer 1 · 2026-03-24 22:04:29

195

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Casimir element of a representation of a semi-simple Lie algebra

Published on 24 Mar 2026 - 22:04

score 930 · Answer 2 · 2026-03-25 03:52:47

930

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dual basis of $\mathfrak{sl}(n,F)$ with respect to the Killing form

Published on 25 Mar 2026 - 3:52

score 78 · Answer 3 · 2026-03-23 20:22:16

78

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Prove that $\mathfrak{sl}(3, F)$ modulo $Z(\mathfrak{sl}(3,F)$ is semisimple

Published on 23 Mar 2026 - 20:22

score 108 · Answer 4 · 2026-02-23 04:55:16

108

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Classification of Continuous Group Homs from Circle to $SL_2(\mathbb{R})$

Published on 23 Feb 2026 - 4:55

score 108 · Answer 5 · 2026-03-26 17:42:31

108

Views

How can I show a the Cartan subalgebra being abelian implies its adjoint representation on the original Lie algebra completely commutes?

Published on 26 Mar 2026 - 17:42

score 189 · Answer 6 · 2026-03-24 18:14:17

189

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Finite dimensional representation of semi-simple Lie algebras are hermitian?

Published on 24 Mar 2026 - 18:14

score 358 · Answer 7 · 2026-02-23 04:42:58

358

Views

Lie algebra cohomology and De Rham cohomology of a compact Lie group

Published on 23 Feb 2026 - 4:42

score 144 · Answer 8 · 2026-03-24 18:37:57

144

Views

Infinite sum of semisimple Ideals of a Lie algebra

Published on 24 Mar 2026 - 18:37

score 448 · Answer 9 · 2026-03-25 03:50:47

448

Views

Do endomorphisms of the adjoint representation of a Lie algebra commute?

Published on 25 Mar 2026 - 3:50

score 377 · Answer 10 · 2026-03-24 20:49:01

377

Views

Why the direct sum of an ideal and its orthogonal is equal to the whole Lie algebra if it is semisimple?

Published on 24 Mar 2026 - 20:49

score 214 · Answer 11 · 2026-03-25 12:34:23

214

Views

How to find the radical of this Lie algebra

Published on 25 Mar 2026 - 12:34

score 416 · Answer 12 · 2026-03-25 13:39:49

416

Views

Help understanding a $\frak {sl}(2)$ Lie algebra representation

Published on 25 Mar 2026 - 13:39

score 382 · Answer 13 · 2026-03-25 02:42:43

382

Views

Subalgebra consisting of nilpotent elements and maximal is conjugate under $\mathscr E(L)$ to $N(\Delta)$

Published on 25 Mar 2026 - 2:42

score 146 · Answer 14 · 2026-03-25 08:34:51

146

Views

Exercise 22.6 in Humphreys Introduction to Lie Algebras and Representation Theory

Published on 25 Mar 2026 - 8:34

score 628 · Answer 15 · 2026-03-25 02:31:08

628

Views

If $x\in L$ lies in exactly one Cartan subalgebra, then $x$ is regular

Published on 25 Mar 2026 - 2:31

List Question

Casimir element of a representation of a semi-simple Lie algebra

dual basis of $\mathfrak{sl}(n,F)$ with respect to the Killing form

Prove that $\mathfrak{sl}(3, F)$ modulo $Z(\mathfrak{sl}(3,F)$ is semisimple

Classification of Continuous Group Homs from Circle to $SL_2(\mathbb{R})$

How can I show a the Cartan subalgebra being abelian implies its adjoint representation on the original Lie algebra completely commutes?

Finite dimensional representation of semi-simple Lie algebras are hermitian?

Lie algebra cohomology and De Rham cohomology of a compact Lie group

Infinite sum of semisimple Ideals of a Lie algebra

Do endomorphisms of the adjoint representation of a Lie algebra commute?

Why the direct sum of an ideal and its orthogonal is equal to the whole Lie algebra if it is semisimple?

How to find the radical of this Lie algebra

Help understanding a $\frak {sl}(2)$ Lie algebra representation

Subalgebra consisting of nilpotent elements and maximal is conjugate under $\mathscr E(L)$ to $N(\Delta)$

Exercise 22.6 in Humphreys Introduction to Lie Algebras and Representation Theory

If $x\in L$ lies in exactly one Cartan subalgebra, then $x$ is regular

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