Question

Do we define the rank of a Lie algebra by using the geometric multiplicity of the zero eigenvalues of the adjoint representation?

score 238 · Answer 1 · 2020-08-26 21:41:55

238

Views

Do we define the rank of a Lie algebra by using the geometric multiplicity of the zero eigenvalues of the adjoint representation?

Published on 26 Aug 2020 - 21:41

score 109 · Answer 2 · 2026-03-21 23:27:41

109

Views

Weights of a faithful representation and roots of $\mathfrak{g}$

Published on 21 Mar 2026 - 23:27

score 86 · Answer 3 · 2020-09-12 21:11:55

86

Views

A root system of vectors in R^n admits a simple system; but does every finite set of vectors

Published on 12 Sep 2020 - 21:11

score 330 · Answer 4 · 2020-09-24 10:06:28

330

Views

Higher-dimensional reflections

Published on 24 Sep 2020 - 10:06

score 425 · Answer 5 · 2026-03-26 09:36:48

425

Views

Which root systems admit a proper root subsystem with full span?

Published on 26 Mar 2026 - 9:36

score 150 · Answer 6 · 2020-10-14 16:48:04

150

Views

Cartan Matrix from commutation relations

Published on 14 Oct 2020 - 16:48

score 47 · Answer 7 · 2020-11-09 15:44:43

47

Views

Showing that $R = \{ \pm(e_i-e_j) : 1 \leq i < j \leq l+1\}$ is a root system

Published on 09 Nov 2020 - 15:44

score 487 · Answer 8 · 2026-03-25 09:28:17

487

Views

How to understand the Galois *-action on a Dynkin diagram

Published on 25 Mar 2026 - 9:28

score 106 · Answer 9 · 2020-11-16 11:46:39

If $\lambda = \sum k_i \alpha_i$ and $P_\lambda \subseteq \cup_{\alpha \in \Phi} P_\alpha \implies \lambda = c\alpha$ for some $\alpha \in \Phi$.

score 62 · Answer 10 · 2020-12-01 18:10:53

62

Views

Positive bases with respect to another fixed base

Published on 01 Dec 2020 - 18:10

score 223 · Answer 11 · 2026-03-25 07:45:58

223

Views

Computational procedure to find the basis of a Lie algebra generated by a finite collection of operators

Published on 25 Mar 2026 - 7:45

score 95 · Answer 12 · 2020-12-18 10:39:59

95

Views

bad primes and torsion primes

Published on 18 Dec 2020 - 10:39

score 435 · Answer 13 · 2026-03-25 06:02:30

435

Views

Computing the longest element of the Weyl group

Published on 25 Mar 2026 - 6:02

score 902 · Answer 14 · 2021-01-01 11:13:15

902

Views

Cartan subalgebras of classical Lie algebras are diagonal matrices

Published on 01 Jan 2021 - 11:13

score 130 · Answer 15 · 2021-01-04 13:29:17

130

Views

Abelian ideals of Borel subalgebra of $\mathfrak{sl}(n)$

Published on 04 Jan 2021 - 13:29

List Question

Do we define the rank of a Lie algebra by using the geometric multiplicity of the zero eigenvalues of the adjoint representation?

Weights of a faithful representation and roots of $\mathfrak{g}$

A root system of vectors in R^n admits a simple system; but does every finite set of vectors

Higher-dimensional reflections

Which root systems admit a proper root subsystem with full span?

Cartan Matrix from commutation relations

Showing that $R = \{ \pm(e_i-e_j) : 1 \leq i < j \leq l+1\}$ is a root system

How to understand the Galois *-action on a Dynkin diagram

If $\lambda = \sum k_i \alpha_i$ and $P_\lambda \subseteq \cup_{\alpha \in \Phi} P_\alpha \implies \lambda = c\alpha$ for some $\alpha \in \Phi$.

Positive bases with respect to another fixed base

Computational procedure to find the basis of a Lie algebra generated by a finite collection of operators

bad primes and torsion primes

Computing the longest element of the Weyl group

Cartan subalgebras of classical Lie algebras are diagonal matrices

Abelian ideals of Borel subalgebra of $\mathfrak{sl}(n)$

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