A quiver is an oriented graph which might contain multiple edges and loops. The terminology is used in representation-theory of finite dimensional algebras, where one considers functors from this graph, viewed as a category, to the category of vector spaces.

learn more… | top users | synonyms

18
votes
2answers
2k views

Why are (representations of ) quivers such a big deal?

Quivers are directed graphs where loops and multi-arrows are allowed. And we can talk about representations of quivers by assigning each vertex a vector space and each arrow a homomorphism. Moreover, ...
7
votes
1answer
188 views

Specific projective dimension of a module over bound quiver

Suppose $K$ is an algebraically closed field, and $A$ is the algebra presented by the quiver $$\require{AMScd} \begin{CD} 1 @>>> 2\\ @V{}VV @V{}VV \\ 3 @>>> 4 @>>> 5 \end{CD}...
4
votes
2answers
144 views

Representations of a quiver and sheaves on P^1

We know from Beilinson that there's an equivalence of derived categories $D^b Rep(Q) \simeq D^b Coh(\mathbb{P}^1)$ where the lefthandside is the derived category of bounded complexes of ...