List questions from semisimple-lie-algebras

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Ideals of semisimple Lie algebras

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A theorem about semisimple Lie algebra

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A Lie algebra with trivial center and commutative radical

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250

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Relation between semisimple Lie Algebras and Killing form

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

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How to tell the rank of a semisimple Lie algebra?

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

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The opposite of Weyl's theorem on Lie algebras

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

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Prove the dual root system is a root system

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

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

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

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133

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Subgraphs of Dynkin Diagrams

Published on 29 Apr 2026 - 12:25

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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