All Questions
Tagged with quivers graph-theory
6
questions
18
votes
1
answer
6k
views
Intersection between category theory and graph theory
I'm a graduate student who has been spending a lot of time working with categories (model categories, derived categories, triangulated categories...) but I used to love graph theory and have always ...
- 25.6k
10
votes
3
answers
1k
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Are the underlying undirected graphs of two mutation-equivalent acylic quivers isomorphic?
Quiver mutation, defined by Fomin and Zelevinsky, is a combinatorial process. It is important in the representation theory of quivers, in the theory of cluster algebras, and in physics.
We consider ...
- 101
6
votes
0
answers
703
views
Tensor product of quivers
As a special case of a general construction I have constructed "accidentally" a tensor product of quivers aka directed multigraphs (aka directed graphs for category theorists). Probably this ...
3
votes
1
answer
212
views
Pairs of paths with the same source and target
Commutative diagrams usually express path equivalences in a category and thus involve pairs of paths in a category with the same source and target.
General diagrams - in categories resp. category ...
- 9,548
3
votes
0
answers
168
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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
0
answers
98
views
When do two path algebras share an underlying graph?
Suppose $Q$ and $Q'$ are two quivers. I am curious as to what relation $\mathbb{C}Q$ bears to $\mathbb{C}Q'$ when $Q$ and $Q'$ share the same underlying graph and only differ by direction.
Since ...
- 420