List questions from representation-theory

Published on 04 Sep 2018 - 19:43

140

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Finding the minimum degree of a representation of an algebra

Published on 05 Sep 2018 - 1:05

208

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Dual of cocyclic module is cyclic

Published on 25 Mar 2026 - 11:19

64

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Please, help me understand tensor products

Published on 06 Sep 2018 - 18:03

99

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Understanding the $\operatorname{Hom}_A(T \otimes_B W, V) \cong \operatorname{Hom}_B(W, \operatorname{Hom}_A(T,V))$ isomorphism?

Published on 26 Mar 2026 - 0:32

51

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Is there an irreducible linear representation of $\mathbb{Z}/2\mathbb{Z} \times \mathbb{Z}/2\mathbb{Z}$ of dimension 2?

Published on 27 Mar 2026 - 4:38

917

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completely reducible module iff intersection of maximal submodules is trivial

Published on 08 Sep 2018 - 1:00

235

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Dual Character for Compact Lie Groups

Published on 25 Mar 2026 - 1:24

215

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Direct sum of Matrix algebras is not isomorphic to some semigroup algebra

Published on 25 Mar 2026 - 1:17

75

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Direct sum of reals and quaternions is not a semigroup algebra for some semigroup

Published on 24 Mar 2026 - 23:48

981

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How to prove the adjoint representation of $\text{SL}_2$ is irreducible when $\text{char}(k) \ne 2$?

Published on 25 Mar 2026 - 9:29

146

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Why is the local polynomial of an Artin representation independent of the choice of the Frobenius element?

Published on 25 Mar 2026 - 3:04

280

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Realization of fundamental weights.

Published on 27 Mar 2026 - 14:45

60

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Show that $R[\mathbb Z/n\mathbb Z] \cong R[x] / (x^n - 1)$

Published on 11 Sep 2018 - 18:31

168

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Geometric Version of Mackey's Theorem

Published on 12 Sep 2018 - 9:44

List Question

The strictly upper triangular "subalgebra" of $M_n(K)$ is not unital?

Finding the minimum degree of a representation of an algebra

Dual of cocyclic module is cyclic

Please, help me understand tensor products

Understanding the $\operatorname{Hom}_A(T \otimes_B W, V) \cong \operatorname{Hom}_B(W, \operatorname{Hom}_A(T,V))$ isomorphism?

Is there an irreducible linear representation of $\mathbb{Z}/2\mathbb{Z} \times \mathbb{Z}/2\mathbb{Z}$ of dimension 2?

completely reducible module iff intersection of maximal submodules is trivial

Dual Character for Compact Lie Groups

Direct sum of Matrix algebras is not isomorphic to some semigroup algebra

Direct sum of reals and quaternions is not a semigroup algebra for some semigroup

How to prove the adjoint representation of $\text{SL}_2$ is irreducible when $\text{char}(k) \ne 2$?

Why is the local polynomial of an Artin representation independent of the choice of the Frobenius element?

Realization of fundamental weights.

Show that $R[\mathbb Z/n\mathbb Z] \cong R[x] / (x^n - 1)$

Geometric Version of Mackey's Theorem

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