Question

For which Lie groups $G$ can one write $g$ as the exponential $\exp X$ of some $X \in {\frak g}$ for every element $g \in G$?

score 999 · Answer 1 · 2026-05-02 14:56:31

999

Views

For which Lie groups $G$ can one write $g$ as the exponential $\exp X$ of some $X \in {\frak g}$ for every element $g \in G$?

Published on 02 May 2026 - 14:56

score 52 · Answer 2 · 2026-05-02 13:54:42

52

Views

Are there proper Ad invariant sets on simple lie algebras?

Published on 02 May 2026 - 13:54

score 613 · Answer 3 · 2026-05-02 19:35:57

613

Views

Center of $\mathfrak{gl}(n,\Bbb F)$ using the adjoint representation

Published on 02 May 2026 - 19:35

score 89 · Answer 4 · 2026-04-13 15:36:57

89

Views

Are there multiple non-isomorphic principal $G$-bundles on Euclidean space?

Published on 13 Apr 2026 - 15:36

score 37 · Answer 5 · 2026-04-14 10:26:23

37

Views

Writing $\mathrm{SO}(2)$ as the zero-set of a function

Published on 14 Apr 2026 - 10:26

score 673 · Answer 6 · 2026-04-30 02:07:25

673

Views

Proving a compact Lie group admits a biinvariant metric

Published on 30 Apr 2026 - 2:07

score 851 · Answer 7 · 2026-04-30 02:07:24

851

Views

Levi-Civita connection with biinvariant metric

Published on 30 Apr 2026 - 2:07

score 464 · Answer 8 · 2026-04-22 16:50:37

464

Views

Ideals of $\mathfrak{gl}_n$

Published on 22 Apr 2026 - 16:50

score 511 · Answer 9 · 2026-04-11 23:22:10

511

Views

Is $U(1)$ a normal subgroup of $U(2)$ and does the question even make sense?

Published on 11 Apr 2026 - 23:22

score 106 · Answer 10 · 2026-05-02 17:32:12

106

Views

Derived Algebra is nilpotent implies the lie algebra is solvable

Published on 02 May 2026 - 17:32

score 1.2k · Answer 11 · 2026-05-02 18:35:07

1.2k

Views

$so(4)$ is isomorphic to $so(3)+so(3)$.

Published on 02 May 2026 - 18:35

score 169 · Answer 12 · 2026-03-30 03:39:10

169

Views

If the Lie algebra is ${\frak g}={\frak a}\oplus{\frak b}$ then the Lie group is $G=AB$?

Published on 30 Mar 2026 - 3:39

score 56 · Answer 13 · 2026-03-29 18:36:05

56

Views

Simply connected linear algebraic group

Published on 29 Mar 2026 - 18:36

score 316 · Answer 14 · 2026-03-25 20:35:20

316

Views

Spheres as Symplectic Homogeneous Spaces

Published on 25 Mar 2026 - 20:35

score 162 · Answer 15 · 2026-05-02 18:35:38

162

Views

Matrix representation of Lie Algebra $B_2$

Published on 02 May 2026 - 18:35

List Question

For which Lie groups $G$ can one write $g$ as the exponential $\exp X$ of some $X \in {\frak g}$ for every element $g \in G$?

Are there proper Ad invariant sets on simple lie algebras?

Center of $\mathfrak{gl}(n,\Bbb F)$ using the adjoint representation

Are there multiple non-isomorphic principal $G$-bundles on Euclidean space?

Writing $\mathrm{SO}(2)$ as the zero-set of a function

Proving a compact Lie group admits a biinvariant metric

Levi-Civita connection with biinvariant metric

Ideals of $\mathfrak{gl}_n$

Is $U(1)$ a normal subgroup of $U(2)$ and does the question even make sense?

Derived Algebra is nilpotent implies the lie algebra is solvable

$so(4)$ is isomorphic to $so(3)+so(3)$.

If the Lie algebra is ${\frak g}={\frak a}\oplus{\frak b}$ then the Lie group is $G=AB$?

Simply connected linear algebraic group

Spheres as Symplectic Homogeneous Spaces

Matrix representation of Lie Algebra $B_2$

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