List questions from semisimple-lie-algebras

Published on 25 Mar 2026 - 10:00

408

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Unique faithful $7$-dimensional representation of semisimple Lie Algebra with $G_2$ root system

Published on 25 Mar 2026 - 11:03

286

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Existence of a non essentially real ideal in a semisimple Lie algebra

Published on 10 Jan 2019 - 1:32

344

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Finding the Weyl group from a Cartan matrix

Published on 25 Mar 2026 - 17:22

1.8k

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Good source of references for the classification of real semisimple Lie algebras

Published on 25 Mar 2026 - 0:54

456

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Is requiring diagonalizable adjoints vacuous in the definition of Cartan subalgebra?

Published on 24 Mar 2026 - 17:18

498

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About nondegeneracy of Killing form

Published on 27 Mar 2026 - 7:16

70

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Is the semisimple part of $x \in L$ belong to $L$ when $L$ is a semisimple Lie algebra?

Published on 24 Mar 2026 - 22:32

271

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How to show this $L$-module is simple? (related to the root space decomposition of semisimle Lie algebras)

Published on 24 Mar 2026 - 23:06

26

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Question about definition related to root system of semisimple Lie algebras

Published on 25 Mar 2026 - 7:53

66

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"If $g$ is semisimple, It is not too hard to see that $H^2(g,a)=0$. With a little supplementary argument..."

Published on 24 Mar 2026 - 18:37

35

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Is this subalgebra semisimple?

Published on 27 Mar 2026 - 6:34

147

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What is known about such dominant integral weights of compact semisimple Lie groups?

Published on 25 Mar 2026 - 11:07

897

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Proving that $G=\mathrm{SL}_d(\mathbb{R})$ is semisimple

Published on 25 Mar 2026 - 3:28

982

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Inner automorphisms of a real semisimple Lie algebra

Published on 25 Mar 2026 - 15:21

List Question

Irreducible Dual Representation

Unique faithful $7$-dimensional representation of semisimple Lie Algebra with $G_2$ root system

Existence of a non essentially real ideal in a semisimple Lie algebra

Finding the Weyl group from a Cartan matrix

Good source of references for the classification of real semisimple Lie algebras

Is requiring diagonalizable adjoints vacuous in the definition of Cartan subalgebra?

About nondegeneracy of Killing form

Is the semisimple part of $x \in L$ belong to $L$ when $L$ is a semisimple Lie algebra?

How to show this $L$-module is simple? (related to the root space decomposition of semisimle Lie algebras)

Question about definition related to root system of semisimple Lie algebras

"If $g$ is semisimple, It is not too hard to see that $H^2(g,a)=0$. With a little supplementary argument..."

Is this subalgebra semisimple?

What is known about such dominant integral weights of compact semisimple Lie groups?

Proving that $G=\mathrm{SL}_d(\mathbb{R})$ is semisimple

Inner automorphisms of a real semisimple Lie algebra

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