Question

Is there an explicit left invariant metric on the general linear group?

score 1.9k · Answer 1 · 2026-04-30 23:17:59

1.9k

Views

Is there an explicit left invariant metric on the general linear group?

Published on 30 Apr 2026 - 23:17

score 665 · Answer 2 · 2026-05-02 19:36:13

665

Views

Cartan subalgebra of ${\frak so}(5)$

Published on 02 May 2026 - 19:36

score 586 · Answer 3 · 2026-04-12 11:10:40

586

Views

Showing that Heisenberg group is a Lie Group.

Published on 12 Apr 2026 - 11:10

score 928 · Answer 4 · 2026-04-11 11:18:10

928

Views

Is a real logarithm of a special orthogonal matrix necessarily skew-symmetric?

Published on 11 Apr 2026 - 11:18

score 51 · Answer 5 · 2026-04-17 03:29:51

51

Views

Let $PSL(3,q)$, $q$ odd. Then for $p \mid q(q^2 - 1)$ and $s \mid q-1$ ($p,s$ prime) we have a $p$-subgroup $X\ne 1$ such that $s$ divides $|N_G(X)|$

Published on 17 Apr 2026 - 3:29

score 955 · Answer 6 · 2026-04-10 21:45:47

955

Views

Are all compact subgroups of $GL(n,\Bbb C)$ in $U(n)$?

Published on 10 Apr 2026 - 21:45

score 485 · Answer 7 · 2026-03-31 07:57:46

485

Views

How can I understand the isomorphism $SO(3)\cong \mathbb{RP}^3 \cong S^3/\mathbb{Z}_2$ and compute the corresponding volumes?

Published on 31 Mar 2026 - 7:57

score 1.3k · Answer 8 · 2026-04-30 02:59:43

1.3k

Views

Proving left-invariance (and proof-verification for right-invariance) for metric constructed from left-invariant Haar measure

Published on 30 Apr 2026 - 2:59

score 447 · Answer 9 · 2026-04-13 23:45:08

447

Views

Why is $\mathbb{S}^1$ not a normal subgroup of $\mathbb{S}^3$

Published on 13 Apr 2026 - 23:45

score 55 · Answer 10 · 2026-04-14 14:57:29

55

Views

Right unidimensional extension of Heisenberg Algebra

Published on 14 Apr 2026 - 14:57

score 149 · Answer 11 · 2026-04-04 11:56:14

149

Views

Proving continuity/smoothness for a special function on a Lie group.

Published on 04 Apr 2026 - 11:56

score 1.4k · Answer 12 · 2026-03-25 23:36:27

1.4k

Views

Spheres as Homogeneous Spaces

Published on 25 Mar 2026 - 23:36

score 175 · Answer 13 · 2026-04-14 03:10:59

175

Views

Lie-group existence on universal covering manifold

Published on 14 Apr 2026 - 3:10

score 275 · Answer 14 · 2026-04-11 11:16:09

275

Views

Good reference on the parametrization of SU(3) and SU(N)

Published on 11 Apr 2026 - 11:16

score 352 · Answer 15 · 2026-04-14 19:05:03

352

Views

Exact sequence for the Spin group

Published on 14 Apr 2026 - 19:05

List Question

Is there an explicit left invariant metric on the general linear group?

Cartan subalgebra of ${\frak so}(5)$

Showing that Heisenberg group is a Lie Group.

Is a real logarithm of a special orthogonal matrix necessarily skew-symmetric?

Let $PSL(3,q)$, $q$ odd. Then for $p \mid q(q^2 - 1)$ and $s \mid q-1$ ($p,s$ prime) we have a $p$-subgroup $X\ne 1$ such that $s$ divides $|N_G(X)|$

Are all compact subgroups of $GL(n,\Bbb C)$ in $U(n)$?

How can I understand the isomorphism $SO(3)\cong \mathbb{RP}^3 \cong S^3/\mathbb{Z}_2$ and compute the corresponding volumes?

Proving left-invariance (and proof-verification for right-invariance) for metric constructed from left-invariant Haar measure

Why is $\mathbb{S}^1$ not a normal subgroup of $\mathbb{S}^3$

Right unidimensional extension of Heisenberg Algebra

Proving continuity/smoothness for a special function on a Lie group.

Spheres as Homogeneous Spaces

Lie-group existence on universal covering manifold

Good reference on the parametrization of SU(3) and SU(N)

Exact sequence for the Spin group

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