Question

Why is $(Ad\, x)^(u)(X) = u(Ad(x^{-1})X)$ for $u\in (T_eG)^$ and $X\in T_eG$?

score 50 · Answer 1 · 2023-06-01 22:43:35

50

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Why is $(Ad\, x)^(u)(X) = u(Ad(x^{-1})X)$ for $u\in (T_eG)^$ and $X\in T_eG$?

Published on 01 Jun 2023 - 22:43

score 245 · Answer 2 · 2026-03-25 23:33:05

245

Views

Salvaging Exercise 3.2.10(2) of Springer's, "Linear Algebraic Groups (Second Edition)".

Published on 25 Mar 2026 - 23:33

score 42 · Answer 3 · 2023-06-05 12:23:50

42

Views

Reference request, relation algebraic groups, real groups and their Lie algebras

Published on 05 Jun 2023 - 12:23

score 71 · Answer 4 · 2026-03-26 06:32:56

71

Views

The associated $X$-bundle to a principal $G$-bundle

Published on 26 Mar 2026 - 6:32

score 43 · Answer 5 · 2023-06-09 19:22:26

43

Views

Maximal torus in the Borel subgroup is maximal in $G$.

Published on 09 Jun 2023 - 19:22

score 81 · Answer 6 · 2026-03-25 08:00:36

81

Views

$PGL_n(F)$ - Where to read about its (structure and) representation theory?

Published on 25 Mar 2026 - 8:00

score 922 · Answer 7 · 2023-06-13 23:30:42

922

Views

What is the connection between algebraic groups and topoi?

Published on 13 Jun 2023 - 23:30

score 106 · Answer 8 · 2026-03-25 22:11:17

106

Views

Complete resource of Ngô's course notes on Algebraic Groups and Group Schemes

Published on 25 Mar 2026 - 22:11

score 122 · Answer 9 · 2026-03-25 23:27:21

122

Views

The torsion subgroup of a diagonalisable linear algebraic group $G$ with ${\rm char}(k)=p$ (alg. closed $k$) is dense in $G$

Published on 25 Mar 2026 - 23:27

score 71 · Answer 10 · 2023-06-29 21:16:12

71

Views

Special orthogonal group and general spin group for non-regular (degenerate) quadratic spaces

Published on 29 Jun 2023 - 21:16

score 40 · Answer 11 · 2023-07-02 12:19:50

40

Views

When is unitary group over ring of integers dense?

Published on 02 Jul 2023 - 12:19

score 43 · Answer 12 · 2023-07-03 11:51:58

43

Views

Quotient of algebraic group by finite subgroup

Published on 03 Jul 2023 - 11:51

score 137 · Answer 13 · 2023-07-04 06:13:06

137

Views

Integrating Homomorphisms of Borel Subalgebras

Published on 04 Jul 2023 - 6:13

score 87 · Answer 14 · 2026-03-25 23:27:21

87

Views

Let $\mathfrak{A}$ be a finite dimensional $k$-algebra for alg. closed $k$. Prove ${\rm Aut}(\mathfrak{A})$ is a closed subgroup of $GL(\mathfrak{A})$

Published on 25 Mar 2026 - 23:27

score 77 · Answer 15 · 2026-03-25 07:45:28

77

Views

Is the quotient group of $2$-th root of unity compact?

Published on 25 Mar 2026 - 7:45

List Question

Why is $(Ad\, x)^(u)(X) = u(Ad(x^{-1})X)$ for $u\in (T_eG)^$ and $X\in T_eG$?

Salvaging Exercise 3.2.10(2) of Springer's, "Linear Algebraic Groups (Second Edition)".

Reference request, relation algebraic groups, real groups and their Lie algebras

The associated $X$-bundle to a principal $G$-bundle

Maximal torus in the Borel subgroup is maximal in $G$.

$PGL_n(F)$ - Where to read about its (structure and) representation theory?

What is the connection between algebraic groups and topoi?

Complete resource of Ngô's course notes on Algebraic Groups and Group Schemes

The torsion subgroup of a diagonalisable linear algebraic group $G$ with ${\rm char}(k)=p$ (alg. closed $k$) is dense in $G$

Special orthogonal group and general spin group for non-regular (degenerate) quadratic spaces

When is unitary group over ring of integers dense?

Quotient of algebraic group by finite subgroup

Integrating Homomorphisms of Borel Subalgebras

Let $\mathfrak{A}$ be a finite dimensional $k$-algebra for alg. closed $k$. Prove ${\rm Aut}(\mathfrak{A})$ is a closed subgroup of $GL(\mathfrak{A})$

Is the quotient group of $2$-th root of unity compact?

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