List questions from semisimple-lie-algebras

Published on 02 Feb 2022 - 17:41

176

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Why is the weight lattice a lattice?

Published on 09 Feb 2022 - 8:22

72

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Show that $\mathfrak{g}_2$ has a dimension $14$ representation

Published on 16 Feb 2022 - 11:57

467

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Baker-Campbell-Hausdorff formula for $ [X,[X,Y]] = [Y,[X,Y]] \neq 0 $

Published on 17 Feb 2022 - 7:51

89

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Unipotent and flag subgroups

Published on 27 Mar 2026 - 3:11

40

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If $\Delta$ is decomposable, why does $\mathfrak{g}$ have a corresponding decomposition into direct sum of ideals.

Published on 27 Mar 2026 - 21:37

396

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All invariant forms of (a representation of) a semi-simple lie group

Published on 23 Feb 2026 - 10:19

132

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Complexification of maximal compact subgroup for complex semisimple Lie group

Published on 01 Mar 2022 - 21:41

113

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When will a complex representation of a semi-simple lie group, have an invariant hermitian form?

Published on 05 Mar 2022 - 22:43

72

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Space of sections of adjoint varieties

Published on 26 Mar 2026 - 17:36

52

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Compact form of $\mathfrak{su}(2)$

Published on 24 Mar 2022 - 17:39

693

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How are weights and roots connected? (In the context of the semisimple Lie algebras)

Published on 27 Mar 2026 - 21:36

145

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Decomposition of universal enveloping algebra of a semisimple Lie algebra

Published on 29 Mar 2022 - 20:41

135

Views

Is there an 'easy' way to see that $\operatorname{Int}_\mathfrak{g}(\mathfrak{k})$ is compact?

Published on 02 Apr 2022 - 4:45

141

Views

Equality between Killing form and a sum over the root space decomposition of a Lie algebra

Published on 07 Apr 2022 - 7:51

List Question

Examples: Infinite-dimensional simple Lie algebras

Why is the weight lattice a lattice?

Show that $\mathfrak{g}_2$ has a dimension $14$ representation

Baker-Campbell-Hausdorff formula for $ [X,[X,Y]] = [Y,[X,Y]] \neq 0 $

Unipotent and flag subgroups

If $\Delta$ is decomposable, why does $\mathfrak{g}$ have a corresponding decomposition into direct sum of ideals.

All invariant forms of (a representation of) a semi-simple lie group

Complexification of maximal compact subgroup for complex semisimple Lie group

When will a complex representation of a semi-simple lie group, have an invariant hermitian form?

Space of sections of adjoint varieties

Compact form of $\mathfrak{su}(2)$

How are weights and roots connected? (In the context of the semisimple Lie algebras)

Decomposition of universal enveloping algebra of a semisimple Lie algebra

Is there an 'easy' way to see that $\operatorname{Int}_\mathfrak{g}(\mathfrak{k})$ is compact?

Equality between Killing form and a sum over the root space decomposition of a Lie algebra

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