Question

In what sense are complex representations of a real Lie algebra and complex representations of the complexified Lie algebra equivalent?

score 1.8k · Answer 1 · 2026-04-14 07:45:48

1.8k

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In what sense are complex representations of a real Lie algebra and complex representations of the complexified Lie algebra equivalent?

Published on 14 Apr 2026 - 7:45

score 462 · Answer 2 · 2026-04-13 18:20:58

462

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Is the fundamental weight basis (a.k.a Dynkin basis) an orthonormal basis?

Published on 13 Apr 2026 - 18:20

score 271 · Answer 3 · 2026-04-12 22:51:53

271

Views

Why do "the Dynkin components of a weight play the role of eigenvalues with respect to the generators $H^i$ of the Cartan subalgebra"?

Published on 12 Apr 2026 - 22:51

score 1k · Answer 4 · 2026-04-14 10:09:05

1k

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General Element of U(4)

Published on 14 Apr 2026 - 10:09

score 4.3k · Answer 5 · 2026-04-14 18:03:36

4.3k

Views

Show that $\mathfrak{sl}(2)$ is a simple Lie algebra

Published on 14 Apr 2026 - 18:03

score 675 · Answer 6 · 2026-04-11 03:51:23

675

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Does the Weyl group act on its Lie algebra?

Published on 11 Apr 2026 - 3:51

score 378 · Answer 7 · 2026-04-15 20:49:14

378

Views

Show that a one dimensional $\mathfrak {g}\!-\!\operatorname{module}$ is irreducible

Published on 15 Apr 2026 - 20:49

score 259 · Answer 8 · 2026-04-17 00:20:13

259

Views

Maximal possible dimension of an abelian Lie subalgebra of Heisenberg Lie algebra of dimension $2n+1$.

Published on 17 Apr 2026 - 0:20

score 424 · Answer 9 · 2026-04-14 14:06:36

424

Views

Why is this not an inconsistency in elementary Lie theory?

Published on 14 Apr 2026 - 14:06

score 160 · Answer 10 · 2026-04-15 05:02:14

160

Views

Relation between compact Lie group and Lie algebra representation

Published on 15 Apr 2026 - 5:02

score 118 · Answer 11 · 2026-04-24 18:29:17

118

Views

Vector field left-invariant then also its respective flow?

Published on 24 Apr 2026 - 18:29

score 92 · Answer 12 · 2026-04-16 11:02:43

92

Views

Condition of solvable Lie algebra.

Published on 16 Apr 2026 - 11:02

score 3.5k · Answer 13 · 2026-04-13 04:29:53

3.5k

Views

Lie Group Structure on the 2-Sphere: does the following argument hold?

Published on 13 Apr 2026 - 4:29

score 264 · Answer 14 · 2026-04-13 14:46:51

264

Views

Calculating central elements of Universal Enveloping Algebras?

Published on 13 Apr 2026 - 14:46

score 1.3k · Answer 15 · 2026-04-14 16:20:39

1.3k

Views

For matrices, why is the Lie algebra equal to the tangent space?

Published on 14 Apr 2026 - 16:20

List Question

In what sense are complex representations of a real Lie algebra and complex representations of the complexified Lie algebra equivalent?

Is the fundamental weight basis (a.k.a Dynkin basis) an orthonormal basis?

Why do "the Dynkin components of a weight play the role of eigenvalues with respect to the generators $H^i$ of the Cartan subalgebra"?

General Element of U(4)

Show that $\mathfrak{sl}(2)$ is a simple Lie algebra

Does the Weyl group act on its Lie algebra?

Show that a one dimensional $\mathfrak {g}\!-\!\operatorname{module}$ is irreducible

Maximal possible dimension of an abelian Lie subalgebra of Heisenberg Lie algebra of dimension $2n+1$.

Why is this not an inconsistency in elementary Lie theory?

Relation between compact Lie group and Lie algebra representation

Vector field left-invariant then also its respective flow?

Condition of solvable Lie algebra.

Lie Group Structure on the 2-Sphere: does the following argument hold?

Calculating central elements of Universal Enveloping Algebras?

For matrices, why is the Lie algebra equal to the tangent space?

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