All Questions
Tagged with quivers co.combinatorics
8 questions
2
votes
0
answers
57
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Number of admissible quotient algebras
Let $Q$ be a finite connected quiver. An admissible quotient algebra is an algebra of the form $KQ/I$ with an admissible ideal $I$.
Question 1: Is there a nice closed formula for the number of ...
- 26.5k
4
votes
0
answers
259
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Road map for learning cluster algebras
I'm a PhD student and I would like learn about cluster algebras. I'm wondering what is a good reference (i.e., has detailed explanations, examples, etc) to learn from the basic and what are some of ...
- 839
2
votes
0
answers
102
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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 ...
- 433
2
votes
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48
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The isomorphism class of the 1-representation of a complete quiver
Let $Q$ be a quiver with vertex set $Q_0$ and the arrows $Q_1$. A quiver self $Q$ is said to be complete if it has no loops and for every arrow in $Q_1$ the opposite arrow is also in $Q_1$.
A ...
- 1,269
2
votes
1
answer
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Cluster algebras of finite type
In the webpage, there is a result:
Theorem 1. Coefficient free cluster algebras without frozen variables are in bijection with Dynkin diagrams of type $A_n$, $B_n$, $C_n$, $D_n$, $E_6, E_7, E_8$, $...
- 6,201
6
votes
2
answers
366
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Is this algebra isomorphic to an incidence algebra?
This question is motivated by trying to establish a converse to Theorem 7.8 of our paper.
I have a finite poset $P$ with the following properties:
$P$ has binary meets (and hence a least element).
$...
- 38.6k
8
votes
3
answers
3k
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quiver mutation
Hello to all,
The phrase "quiver mutation has been invented by Fomin and Zelevinsky and has found numerous applications throughout mathematics and physics" is one that some of us encountered on a ...
10
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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 ...
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