All Questions
Tagged with quivers linear-algebra
5
questions
12
votes
2
answers
767
views
Matrices into path algebras
I was thinking about quivers recently, and the following idea came to me.
Let ei,j denote the matrix unit in Mn for 1 ≤ i,j ≤ n. Let Γ denote the complete quiver on vertices {1, …,...
- 1,726
5
votes
3
answers
763
views
Acyclic quivers differing only in arrow directions: functorial isomorphism of representation categories?
Let $Q$ and $R$ be two acyclic quivers which differ only in the directions of their arrows (i. e., the underlying undirected graphs are the same).
1. Does there exist an isomorphism of additive ...
- 32.7k
3
votes
0
answers
168
views
A conceptual explanation for the Kirchoff matrix theorem in terms of the quiver algebra
On the wikipedia page for the Kirchoff matrix theorem, they state a souped up version of the theorem:
Let $G$ be a finite undirected loopless graph and let us form the square matrix $L$ indexed by the ...
- 7,498
2
votes
1
answer
279
views
Indecomposable extensions of regular simple modules by preprojectives
Given four points in general position on $\mathbb{P}^2$ there exists a projection to $\mathbb{P}^1$ collapsing these four pairwise to two points. Its kernel is some fifth point on $\mathbb{P}^2$.
In ...
- 843
2
votes
0
answers
70
views
Isomorphic quiver representations "after adding some zeros"
Let $Q$ be a quiver, with dimension vector $d$ and let $e$ be another dimension vector, such that $d_v\leq e_v$ for every vertex $v$ of $Q$. If $M$ is a $K$-representation of $Q$ of dimension vector $...
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