List questions from root-systems

Published on 25 Mar 2026 - 22:09

137

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Construction of the $E_8$ root system

Published on 18 Apr 2020 - 1:10

202

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If the Weyl group $\mathcal W$ is a normal subgroup of $\mathrm{Aut}(\Phi)$, how can the Weyl group of $A_2$ be dihedral of order $6$?

Published on 01 May 2020 - 0:49

459

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Classification of non-simple Lie algebras

Published on 09 May 2020 - 12:07

444

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Isomorphism between root systems: why not assume isometry?

Published on 14 May 2020 - 15:03

1.4k

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There are no semisimple Lie algebras of dimension $4$, $5$, or $7$

Published on 22 May 2020 - 12:24

68

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Meanings of root system: Show definitions/intuitions and $Λ_{root} ⊂ Λ_{char} ⊂ Λ_{weight}?$

Published on 30 May 2020 - 17:13

207

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Lie Algebras: Root algorithm for the positive roots of $G_2$

Published on 25 Jun 2020 - 0:45

672

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$SO(p,q)$ Fundamental Weights?

Published on 28 Jun 2020 - 20:42

145

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Constructing the root diagram for $B_2$

Published on 25 Mar 2026 - 3:05

196

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If $\lambda \prec \eta$ are positive roots, then there exists another root $\zeta$ such that $\lambda \prec \zeta \prec \eta$.

Published on 05 Jul 2020 - 4:25

60

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Determine whether a set of vectors forms a root system

Published on 10 Jul 2020 - 19:14

73

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A problem on two bases $\Delta$ and $\Delta'$ of a root system

Published on 28 Jul 2020 - 12:25

92

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Number of ways of expressing a weight as a sum of positive roots

Published on 31 Jul 2020 - 8:43

294

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Perfect pairing co-weight lattice and root lattice

Published on 20 Jul 2016 - 8:20

List Question

Brent's Method convergence criteria

Construction of the $E_8$ root system

If the Weyl group $\mathcal W$ is a normal subgroup of $\mathrm{Aut}(\Phi)$, how can the Weyl group of $A_2$ be dihedral of order $6$?

Classification of non-simple Lie algebras

Isomorphism between root systems: why not assume isometry?

There are no semisimple Lie algebras of dimension $4$, $5$, or $7$

Meanings of root system: Show definitions/intuitions and $Λ_{root} ⊂ Λ_{char} ⊂ Λ_{weight}?$

Lie Algebras: Root algorithm for the positive roots of $G_2$

$SO(p,q)$ Fundamental Weights?

Constructing the root diagram for $B_2$

If $\lambda \prec \eta$ are positive roots, then there exists another root $\zeta$ such that $\lambda \prec \zeta \prec \eta$.

Determine whether a set of vectors forms a root system

A problem on two bases $\Delta$ and $\Delta'$ of a root system

Number of ways of expressing a weight as a sum of positive roots

Perfect pairing co-weight lattice and root lattice

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