All Questions
Tagged with quivers derived-categories
9 questions
3
votes
0
answers
102
views
Projective resolution of a quiver with relations
How do we compute the projective resolution of a representation of a quiver with relations.
For example consider the Beilinson quiver $B_4$
$.
with the relations $\{\alpha_j^k\alpha_i^{k-1}=\alpha_i^...
- 179
12
votes
1
answer
577
views
Embedding of a derived category into another derived category
I am considering the following two cases:
Assume that there is an embedding: $D^b(\mathcal{A})\xrightarrow{\Phi} D^b(\mathbb{P}^2)$and the homological dimension of $\mathcal{A}$ is equal to $1$($\...
- 1,982
8
votes
1
answer
663
views
References for quivers and derived categories of coherent sheaves for a string theory student
I'm a student mostly from physics knowledge hoping to learn about the math involved the string theory paper Topological Quiver Matrix Models and Quantum Foam.
Context: The topological string theory ...
- 502
4
votes
1
answer
731
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Graded quivers vs "ordinary" quivers and derived categories
I have heard the "slogan" that graded quivers are (derived) equivalent to ordinary quivers (with this "result" being attributed to Keller) and am looking for a precise statement and a reference.
By a ...
- 1,211
2
votes
0
answers
42
views
Predecessors and Successors of regular silting objects in bounded derived categories of wild hereditary algebras
Let $\Lambda$ be a wild hereditary algebra and let $T$ be one of its regular silting objects (i.e. all indecomposable direct summands of $T$ are shifts of indecomposable regular modules). What do we ...
- 417
4
votes
0
answers
199
views
Short proof of the classification of representation-finite symmetric algebras up to stable equivalence
Assume $K$ is an algebraically closed field and $A$ a finite dimensional $K$-algebra. Assume additionally that $A$ is symmetric and representation-finite.
Then one has the following classification of ...
- 26.5k
10
votes
2
answers
2k
views
Derived category of varieties and derived category of quiver algebras
I have heard that derived category of coherent sheaves $\mathrm{Coh}(X)$ on any Fano varieties $X$ may be realized as derived category $\mathrm{Coh}(\mathrm{Rep}(Q,W))$ of representation of quiver $Q$ ...
- 103
13
votes
0
answers
615
views
The derived category of integral representations of a Dynkin quiver
Let $Q$ be a Dynkin quiver. Let $\mathbb CQ$ be its complex path algebra. It is defined in a way such that modules over $\mathbb CQ$ are the same as representations of the quiver $Q$. Let's write $\...
- 3,174
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 ...
- 101