Question

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

score 322 · Answer 1 · 2026-03-17 22:29:18

322

Views

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

Published on 17 Mar 2026 - 22:29

score 183 · Answer 2 · 2026-03-19 20:34:28

183

Views

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

Published on 19 Mar 2026 - 20:34

score 94 · Answer 3 · 2026-03-17 07:38:01

94

Views

Action of Unipotent algebraic group

Published on 17 Mar 2026 - 7:38

score 77 · Answer 4 · 2026-03-21 08:39:35

77

Views

From a compact topological group to a commutative Hopf algebra

Published on 21 Mar 2026 - 8:39

score 59 · Answer 5 · 2026-03-17 16:52:15

59

Views

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

Published on 17 Mar 2026 - 16:52

score 317 · Answer 6 · 2026-03-17 04:53:14

317

Views

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

Published on 17 Mar 2026 - 4:53

score 174 · Answer 7 · 2026-03-17 06:11:19

174

Views

Is the product of simply connected algebraic groups simply connected?

Published on 17 Mar 2026 - 6:11

score 45 · Answer 8 · 2026-03-17 08:55:00

45

Views

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

Published on 17 Mar 2026 - 8:55

score 87 · Answer 9 · 2026-03-17 06:55:04

87

Views

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

Published on 17 Mar 2026 - 6:55

score 434 · Answer 10 · 2026-03-22 08:56:41

434

Views

Book recommendation for Hopf algebras

Published on 22 Mar 2026 - 8:56

score 189 · Answer 11 · 2026-03-20 06:52:45

189

Views

Why isn't $ \alpha_p $ smooth?

Published on 20 Mar 2026 - 6:52

score 219 · Answer 12 · 2026-03-20 01:50:09

219

Views

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

Published on 20 Mar 2026 - 1:50

score 115 · Answer 13 · 2026-03-20 09:40:37

115

Views

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

Published on 20 Mar 2026 - 9:40

score 224 · Answer 14 · 2026-03-21 04:12:17

224

Views

Is algebraic closure necessary for Rosenlicht's Theorem?

Published on 21 Mar 2026 - 4:12

score 55 · Answer 15 · 2026-03-20 20:50:21

55

Views

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

Published on 20 Mar 2026 - 20:50

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 $k$.

Trending Questions

Popular # Hahtags

Popular Questions