List questions from semisimple-lie-algebras

Published on 22 Mar 2026 - 14:11

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Ideals of semisimple Lie algebras

Published on 25 Mar 2026 - 7:21

346

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A theorem about semisimple Lie algebra

Published on 25 Mar 2026 - 0:19

367

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A Lie algebra with trivial center and commutative radical

Published on 17 Mar 2026 - 10:48

245

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Relation between semisimple Lie Algebras and Killing form

Published on 25 Mar 2026 - 10:08

136

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If $\mathfrak{g}$ is a semisimple $\Rightarrow$ $\mathfrak{h} \subset \mathfrak{g} $ imply $\mathfrak{h} \cap \mathfrak{h}^\perp = \{0\}$

Published on 17 Mar 2026 - 18:06

3k

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How to tell the rank of a semisimple Lie algebra?

Published on 25 Mar 2026 - 2:24

200

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If $H$ is a maximal toral subalgebra of $L$, then $H = H_1 \oplus ... \oplus H_t,$ where $H_i = L_i \cap H$.

Published on 16 Mar 2026 - 23:56

341

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The opposite of Weyl's theorem on Lie algebras

Published on 17 Mar 2026 - 3:48

470

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Show that the semisimple and nilpotent parts of $x \in L$ are the sums of the semisimple and nilpotent parts

Published on 17 Mar 2026 - 15:06

1.1k

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Prove the dual root system is a root system

Published on 25 Mar 2026 - 7:34

704

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Finite dimensional irreducible representations of a semisimple Lie Algebra separate points of the universal enveloping algebra.

Published on 17 Mar 2026 - 1:28

195

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$(V,\rho)$ irreducible, im $\rho \subset \mathfrak{sl}_n$, then $\mathfrak{g}$ is semisimple

Published on 17 Mar 2026 - 18:10

677

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Which roots are fixed by simple reflections of the Weyl Group?

Published on 24 Mar 2026 - 22:01

125

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Subgraphs of Dynkin Diagrams

Published on 25 Mar 2026 - 10:03

List Question

Why is a root system called a "root" system?

Ideals of semisimple Lie algebras

A theorem about semisimple Lie algebra

A Lie algebra with trivial center and commutative radical

Relation between semisimple Lie Algebras and Killing form

If $\mathfrak{g}$ is a semisimple $\Rightarrow$ $\mathfrak{h} \subset \mathfrak{g} $ imply $\mathfrak{h} \cap \mathfrak{h}^\perp = \{0\}$

How to tell the rank of a semisimple Lie algebra?

If $H$ is a maximal toral subalgebra of $L$, then $H = H_1 \oplus ... \oplus H_t,$ where $H_i = L_i \cap H$.

The opposite of Weyl's theorem on Lie algebras

Show that the semisimple and nilpotent parts of $x \in L$ are the sums of the semisimple and nilpotent parts

Prove the dual root system is a root system

Finite dimensional irreducible representations of a semisimple Lie Algebra separate points of the universal enveloping algebra.

$(V,\rho)$ irreducible, im $\rho \subset \mathfrak{sl}_n$, then $\mathfrak{g}$ is semisimple

Which roots are fixed by simple reflections of the Weyl Group?

Subgraphs of Dynkin Diagrams

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