Question

Identifying homomorphisms between the root spaces and the dual space of a Lie algebra via the Cartan-Killing form

score 75 · Answer 1 · 2022-04-12 09:53:24

75

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Identifying homomorphisms between the root spaces and the dual space of a Lie algebra via the Cartan-Killing form

Published on 12 Apr 2022 - 9:53

score 36 · Answer 2 · 2022-04-18 11:55:43

36

Views

Isomorphism $\operatorname{Ext}(B,A) \cong H^1(\mathfrak{g}, \operatorname{Hom}(B,A))$

Published on 18 Apr 2022 - 11:55

score 305 · Answer 3 · 2026-02-23 04:57:24

305

Views

Explicit matrices $h_\alpha$ that correspond to the long roots $\alpha$ in a classical compact simple Lie algebra over the reals

Published on 23 Feb 2026 - 4:57

score 88 · Answer 4 · 2026-03-25 09:22:35

88

Views

Lie algebra structure on $\mathbb{C}[G]$

Published on 25 Mar 2026 - 9:22

score 146 · Answer 5 · 2026-02-28 00:03:19

146

Views

Set of weights of dual representation $V^*$ in terms of weights of $V$

Published on 28 Feb 2026 - 0:03

score 336 · Answer 6 · 2026-02-28 00:01:56

336

Views

Decomposing tensor products of $\mathfrak{so}(2n)$-representations

Published on 28 Feb 2026 - 0:01

score 178 · Answer 7 · 2026-03-27 23:19:58

178

Views

Root system for Lie algebras: If $\alpha, \beta, \alpha - \beta \in \Phi$ are all roots, is $(\alpha, \beta) > 0$?

Published on 27 Mar 2026 - 23:19

score 183 · Answer 8 · 2022-05-21 13:39:28

183

Views

Constructing semisimple Lie algebras of dimension $n$

Published on 21 May 2022 - 13:39

score 79 · Answer 9 · 2022-06-07 18:04:51

79

Views

Semisimple 6-dimensional Lie Algebra

Published on 07 Jun 2022 - 18:04

score 621 · Answer 10 · 2022-06-12 11:18:52

621

Views

What is the importance of Cartan decomposition of a semi-simple Lie algebra?

Published on 12 Jun 2022 - 11:18

score 245 · Answer 11 · 2022-06-20 01:12:54

245

Views

Are infinite-dimensional representations of semisimple Lie algebras semisimple?

Published on 20 Jun 2022 - 1:12

score 119 · Answer 12 · 2026-03-25 09:20:36

119

Views

Question concerning positive Weyl chamber

Published on 25 Mar 2026 - 9:20

score 30 · Answer 13 · 2022-06-22 10:51:37

30

Views

Semisimple Lie algebra coincides with its commutant

Published on 22 Jun 2022 - 10:51

score 79 · Answer 14 · 2022-07-02 10:49:50

79

Views

Prove that raising operator on non-highest weight is non-zero

Published on 02 Jul 2022 - 10:49

score 141 · Answer 15 · 2022-07-03 13:09:15

141

Views

All weight spaces are 1 dimensional implies representation is irreducible for $\mathfrak{sl}(2,\mathbb{C})$?

Published on 03 Jul 2022 - 13:09

List Question

Identifying homomorphisms between the root spaces and the dual space of a Lie algebra via the Cartan-Killing form

Isomorphism $\operatorname{Ext}(B,A) \cong H^1(\mathfrak{g}, \operatorname{Hom}(B,A))$

Explicit matrices $h_\alpha$ that correspond to the long roots $\alpha$ in a classical compact simple Lie algebra over the reals

Lie algebra structure on $\mathbb{C}[G]$

Set of weights of dual representation $V^*$ in terms of weights of $V$

Decomposing tensor products of $\mathfrak{so}(2n)$-representations

Root system for Lie algebras: If $\alpha, \beta, \alpha - \beta \in \Phi$ are all roots, is $(\alpha, \beta) > 0$?

Constructing semisimple Lie algebras of dimension $n$

Semisimple 6-dimensional Lie Algebra

What is the importance of Cartan decomposition of a semi-simple Lie algebra?

Are infinite-dimensional representations of semisimple Lie algebras semisimple?

Question concerning positive Weyl chamber

Semisimple Lie algebra coincides with its commutant

Prove that raising operator on non-highest weight is non-zero

All weight spaces are 1 dimensional implies representation is irreducible for $\mathfrak{sl}(2,\mathbb{C})$?

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