Question

How does studying the complexified Lie algebra $\mathfrak{g}_\mathbb{C}$ help us understand the original Lie algebra $\mathfrak{g}$?

score 607 · Answer 1 · 2018-06-09 09:24:58

How does studying the complexified Lie algebra $\mathfrak{g}_\mathbb{C}$ help us understand the original Lie algebra $\mathfrak{g}$?

score 1.4k · Answer 2 · 2026-03-23 13:31:49

1.4k

Views

What is the order of the Weyl group?

Published on 23 Mar 2026 - 13:31

score 229 · Answer 3 · 2026-03-25 17:42:10

229

Views

Proving the exponent of an element of a the Lie Algebra is an element of the Lie group.

Published on 25 Mar 2026 - 17:42

score 212 · Answer 4 · 2018-06-10 18:58:56

212

Views

Finite-dimensional irreducible representation with non-vanishing zero weight space

Published on 10 Jun 2018 - 18:58

score 884 · Answer 5 · 2018-06-14 19:55:43

884

Views

Obtaining representation of a real Lie algebra from the complexification "by restriction"

Published on 14 Jun 2018 - 19:55

score 90 · Answer 6 · 2026-03-25 07:48:33

90

Views

Are all real forms of an algebraic Lie algebra algebraic?

Published on 25 Mar 2026 - 7:48

score 568 · Answer 7 · 2018-06-16 12:10:57

568

Views

Is there a way to determine the prefactor of the trace of the product of two $SU(N)$ matrices?

Published on 16 Jun 2018 - 12:10

score 326 · Answer 8 · 2018-06-16 22:14:54

326

Views

Connected Subgroups of $SL(2,\mathbb{R})$

Published on 16 Jun 2018 - 22:14

score 62 · Answer 9 · 2018-06-18 16:41:21

62

Views

Relation between representations and roots, weights

Published on 18 Jun 2018 - 16:41

score 140 · Answer 10 · 2018-06-19 07:40:25

140

Views

Unique Lie subgroup structure

Published on 19 Jun 2018 - 7:40

score 159 · Answer 11 · 2026-03-22 05:52:20

159

Views

q-quantization of Lie bialgebras

Published on 22 Mar 2026 - 5:52

score 461 · Answer 12 · 2026-03-25 06:12:18

461

Views

Cartan subalgebra and orbits of the adjoint action

Published on 25 Mar 2026 - 6:12

score 34 · Answer 13 · 2026-03-25 04:42:44

34

Views

Equivalence of categroies between representations of $\operatorname{Sp}(2g;\mathbb{Q})$ and $\mathfrak{sp}(2g;\mathbb{Q})$.

Published on 25 Mar 2026 - 4:42

score 1.1k · Answer 14 · 2018-06-23 18:00:42

1.1k

Views

Obtaining Weights of Tensor Product representations of Lie Algebra

Published on 23 Jun 2018 - 18:00

score 632 · Answer 15 · 2026-02-22 23:28:45

632

Views

How to recover the covariant derivative from the pull back from that on the principal bundle

Published on 22 Feb 2026 - 23:28

List Question

How does studying the complexified Lie algebra $\mathfrak{g}_\mathbb{C}$ help us understand the original Lie algebra $\mathfrak{g}$?

What is the order of the Weyl group?

Proving the exponent of an element of a the Lie Algebra is an element of the Lie group.

Finite-dimensional irreducible representation with non-vanishing zero weight space

Obtaining representation of a real Lie algebra from the complexification "by restriction"

Are all real forms of an algebraic Lie algebra algebraic?

Is there a way to determine the prefactor of the trace of the product of two $SU(N)$ matrices?

Connected Subgroups of $SL(2,\mathbb{R})$

Relation between representations and roots, weights

Unique Lie subgroup structure

q-quantization of Lie bialgebras

Cartan subalgebra and orbits of the adjoint action

Equivalence of categroies between representations of $\operatorname{Sp}(2g;\mathbb{Q})$ and $\mathfrak{sp}(2g;\mathbb{Q})$.

Obtaining Weights of Tensor Product representations of Lie Algebra

How to recover the covariant derivative from the pull back from that on the principal bundle

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