3
votes
1answer
390 views

Wedderburn decomposition of $D_{5}$

This is crossposted from MSE. The question: Find the Wedderburn decomposition of $D_{5},$ the dihedral group of order 10, over the field $\mathbb{F}_{3}.$ I have shown that the irreducible ...
2
votes
0answers
103 views

Quivers for algebras which are not basic or unital.

Are there any definitions of quivers for algebras which are not basic or unital? I am reading the book Elements of the representation theory of associative algebras: volume one. The ordinary quivers ...
3
votes
1answer
276 views

Character theory of $2$-Frobenius groups.

This is a crosspost of my (slightly longer) question on MSE since I'm not getting any responses there. Definition. Let $G$ be a finite group and $F_1=\text{Fit}\,G$ and ...
1
vote
1answer
292 views

Question about the shape of the dual module of a module

Hi, I am reading this paper and have the following question:. On page 5 you can see different types of $A_n$-modules ($\ A_n=k[x,y]/\langle x^2,y^{n+2},xy^{n+1}\rangle\ $)$\ $ and later in the paper ...
1
vote
1answer
240 views

Defect groups and subgroups

I have asked this question on Stack Exchange but had no response; it's been bugging me for a few days. I am struggling to see how to apply Mackey's theorem to prove a certain Lemma in Local ...