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2 votes
0 answers
57 views

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 ...
2 votes
1 answer
315 views

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 votes
2 answers
366 views

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). $...
10 votes
3 answers
1k views

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 ...