Question

How do you prove that category of representations of $G_m$ is equivalent to the category of finite dimensional graded vector spaces?

score 332 · Answer 1 · 2026-05-06 04:22:01

332

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How do you prove that category of representations of $G_m$ is equivalent to the category of finite dimensional graded vector spaces?

Published on 06 May 2026 - 4:22

score 191 · Answer 2 · 2026-05-04 23:46:54

191

Views

How to realize the character group as a Lie/algebraic/topological group?

Published on 04 May 2026 - 23:46

score 101 · Answer 3 · 2026-05-05 11:45:08

101

Views

Action of Unipotent algebraic group

Published on 05 May 2026 - 11:45

score 85 · Answer 4 · 2026-05-05 18:12:40

85

Views

From a compact topological group to a commutative Hopf algebra

Published on 05 May 2026 - 18:12

score 64 · Answer 5 · 2026-05-05 17:06:33

64

Views

When do we have $C(G) \otimes C(G) =C(G\times G)?$

Published on 05 May 2026 - 17:06

score 322 · Answer 6 · 2026-05-05 08:40:37

322

Views

What is the internal Hom object in the category $\mathcal{C} = \mathbf{Rep}_k(G)$?

Published on 05 May 2026 - 8:40

score 184 · Answer 7 · 2026-04-29 12:44:03

184

Views

Is the product of simply connected algebraic groups simply connected?

Published on 29 Apr 2026 - 12:44

score 52 · Answer 8 · 2026-05-04 21:48:53

52

Views

Connected subgroup of $(K^\times)^n$ of Zariski dimension 1

Published on 04 May 2026 - 21:48

score 93 · Answer 9 · 2026-05-04 19:13:56

93

Views

Action of $ \mathbb{G}_m $ on $ \mathbb{A}^n $ by multiplication.

Published on 04 May 2026 - 19:13

score 440 · Answer 10 · 2026-05-05 19:30:25

440

Views

Book recommendation for Hopf algebras

Published on 05 May 2026 - 19:30

score 194 · Answer 11 · 2026-05-10 12:14:04

194

Views

Why isn't $ \alpha_p $ smooth?

Published on 10 May 2026 - 12:14

score 225 · Answer 12 · 2026-04-29 12:43:54

225

Views

Why is any coarse moduli space for hypersurfaces is a categorical quotient?

Published on 29 Apr 2026 - 12:43

score 122 · Answer 13 · 2026-04-29 12:41:10

122

Views

Schubert variety associated to a flag of subspaces of a vector space

Published on 29 Apr 2026 - 12:41

score 229 · Answer 14 · 2026-05-10 12:15:53

229

Views

Is algebraic closure necessary for Rosenlicht's Theorem?

Published on 10 May 2026 - 12:15

score 59 · Answer 15 · 2026-04-29 12:43:40

59

Views

Question about the equivalence between the categories of affine group schemes and Hopf algebras over $k$.

Published on 29 Apr 2026 - 12:43

List Question

How do you prove that category of representations of $G_m$ is equivalent to the category of finite dimensional graded vector spaces?

How to realize the character group as a Lie/algebraic/topological group?

Action of Unipotent algebraic group

From a compact topological group to a commutative Hopf algebra

When do we have $C(G) \otimes C(G) =C(G\times G)?$

What is the internal Hom object in the category $\mathcal{C} = \mathbf{Rep}_k(G)$?

Is the product of simply connected algebraic groups simply connected?

Connected subgroup of $(K^\times)^n$ of Zariski dimension 1

Action of $ \mathbb{G}_m $ on $ \mathbb{A}^n $ by multiplication.

Book recommendation for Hopf algebras

Why isn't $ \alpha_p $ smooth?

Why is any coarse moduli space for hypersurfaces is a categorical quotient?

Schubert variety associated to a flag of subspaces of a vector space

Is algebraic closure necessary for Rosenlicht's Theorem?

Question about the equivalence between the categories of affine group schemes and Hopf algebras over $k$.

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